9c:I[416523,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"ScrollArea"] d4:I[776218,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"Button"] 36:o1,~36:o93a,1:"$Sreact.fragment" 2:I[642832,["/_next/static/immutable/chunks/2_93dzz8su_du.js"],"default"] 3:I[796895,["/_next/static/immutable/chunks/2_93dzz8su_du.js"],"default"] 5:I[642832,["/_next/static/immutable/chunks/2_93dzz8su_du.js"],"LoadingBoundaryProvider"] 6:"$Sreact.suspense" 8:I[549811,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js"],"SearchContextProvider"] 9:I[833710,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js"],"ContentViewsProvider"] a:I[912054,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js"],"AiContextProvider"] :HL["/_next/static/immutable/chunks/3venc96ftp0af.css","style"] :HL["/_next/static/immutable/chunks/1dhohn6aqwiy7.css","style"] 23:X 24:X 25:X 26:X 27:X 28:X 2a:X 2b:X 2c:X 36:o170f,0:{"f":[[["",{"children":[["locale","en","d",[".well-known","api","llms.mdx","llms.txt","mcp","og","rss.xml","sitemap","sitemap.xml","skill.md"]],{"children":["(app)",{"children":["(shared)",{"children":["(main)",{"children":["(learn)",{"children":["materials",{"children":[["subject","mathematics","d",[]],{"children":[["topic","complex-number","d",[]],{"children":[["lesson","multiplication-complex-numbers","oc",[]],{"children":["__PAGE__?{\"ctx\":\"merdeka~class-11-mathematics-complex-number\"}",{},"$undefined","$undefined",162]},"$undefined","$undefined",98]},"$undefined","$undefined",98]},"$undefined","$undefined",98]},"$undefined","$undefined",98]},"$undefined","$undefined",98]},"$undefined","$undefined",98]},"$undefined","$undefined",98]},"$undefined","$undefined",70]},"$undefined","$undefined",58]},"$undefined","$undefined",90],[["$","$1","c",{"children":[null,["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":[[["$","title",null,{"children":"404: This page could not be found."}],["$","div",null,{"style":{"fontFamily":"system-ui,\"Segoe UI\",Roboto,Helvetica,Arial,sans-serif,\"Apple Color Emoji\",\"Segoe UI Emoji\"","height":"100vh","textAlign":"center","display":"flex","flexDirection":"column","alignItems":"center","justifyContent":"center"},"children":["$","div",null,{"children":[["$","style",null,{"dangerouslySetInnerHTML":{"__html":"body{color:#000;background:#fff;margin:0}.next-error-h1{border-right:1px solid rgba(0,0,0,.3)}@media (prefers-color-scheme:dark){body{color:#fff;background:#000}.next-error-h1{border-right:1px solid rgba(255,255,255,.3)}}"}}],["$","h1",null,{"className":"next-error-h1","style":{"display":"inline-block","margin":"0 20px 0 0","padding":"0 23px 0 0","fontSize":24,"fontWeight":500,"verticalAlign":"top","lineHeight":"49px"},"children":404}],["$","div",null,{"style":{"display":"inline-block"},"children":["$","h2",null,{"style":{"fontSize":14,"fontWeight":400,"lineHeight":"49px","margin":0},"children":"This page could not be found."}]}]]}]}]],[]],"forbidden":"$undefined","unauthorized":"$undefined"}]]}],{"children":[["$","$1","c",{"children":[[["$","link","0",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/3venc96ftp0af.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","link","1",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/1dhohn6aqwiy7.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","script","script-0",{"src":"/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","async":true,"nonce":"$undefined"}],["$","script","script-1",{"src":"/_next/static/immutable/chunks/1u94c24vqx26q.js","async":true,"nonce":"$undefined"}],["$","script","script-2",{"src":"/_next/static/immutable/chunks/44psnuid4hcf5.js","async":true,"nonce":"$undefined"}],["$","script","script-3",{"src":"/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","async":true,"nonce":"$undefined"}],["$","script","script-4",{"src":"/_next/static/immutable/chunks/0ni87mxribyly.js","async":true,"nonce":"$undefined"}]],"$L4"]}],{"children":[["$","$L5",null,{"loading":[["$","div","l",{"className":"min-h-svh bg-background"}],[],null],"children":["$","$1","c",{"children":[[["$","script","script-0",{"src":"/_next/static/immutable/chunks/0g7ln_b7f132w.js","async":true,"nonce":"$undefined"}],["$","script","script-1",{"src":"/_next/static/immutable/chunks/1bapa2m2ksez8.js","async":true,"nonce":"$undefined"}],["$","script","script-2",{"src":"/_next/static/immutable/chunks/0ugejllqhnrwj.js","async":true,"nonce":"$undefined"}],["$","script","script-3",{"src":"/_next/static/immutable/chunks/1gze7y7ht-33b.js","async":true,"nonce":"$undefined"}],["$","script","script-4",{"src":"/_next/static/immutable/chunks/393_w_-eb8uv-.js","async":true,"nonce":"$undefined"}]],["$","$6",null,{"fallback":null,"children":"$L7"}]]}]}],{"children":[["$","$1","c",{"children":[[["$","script","script-0",{"src":"/_next/static/immutable/chunks/0chv-zggdaw_f.js","async":true,"nonce":"$undefined"}],["$","script","script-1",{"src":"/_next/static/immutable/chunks/287vic71a6h_7.js","async":true,"nonce":"$undefined"}]],["$","$L8",null,{"children":["$","$L9",null,{"children":["$","$La",null,{"children":["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]}]}]}]]}],{"children":[["$","$1","c",{"children":[[["$","script","script-0",{"src":"/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","async":true,"nonce":"$undefined"}],["$","script","script-1",{"src":"/_next/static/immutable/chunks/136a_3pwwx3sd.js","async":true,"nonce":"$undefined"}],["$","script","script-2",{"src":"/_next/static/immutable/chunks/1j7t38u2zaqis.js","async":true,"nonce":"$undefined"}],["$","script","script-3",{"src":"/_next/static/immutable/chunks/02shfbk-zzfca.js","async":true,"nonce":"$undefined"}],["$","script","script-4",{"src":"/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","async":true,"nonce":"$undefined"}],"$Lb","$Lc","$Ld","$Le","$Lf","$L10","$L11","$L12","$L13","$L14","$L15","$L16","$L17","$L18","$L19","$L1a","$L1b"],"$L1c"]}],{"children":["$L1d",{"children":["$L1e",{"children":["$L1f",{"children":["$L20",{"children":["$L21",{"children":["$L22",{},null,false,"$23"]},null,false,"$24"]},null,false,"$24"]},null,false,"$24"]},null,false,"$24"]},null,false,"$24"]},null,false,"$25"]},null,false,"$26"]},null,false,"$27"]},null,false,"$28"]},null,false,"$24"],"$L29",false]],"q":"?ctx=merdeka~class-11-mathematics-complex-number","i":false,"S":false,"h":"$2a","r":"$2b","s":"$2c","a":"$@2d","u":"$@2e"} 36:o6c0,2f:I[150664,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js"],"AppShell",1] 36:o1000,31:I[819602,["/_next/static/immutable/chunks/2_93dzz8su_du.js"],"OutletBoundary"] 33:I[819602,["/_next/static/immutable/chunks/2_93dzz8su_du.js"],"ViewportBoundary"] 35:I[819602,["/_next/static/immutable/chunks/2_93dzz8su_du.js"],"MetadataBoundary"] b:["$","script","script-5",{"src":"/_next/static/immutable/chunks/1k-yr9yysem7x.js","async":true,"nonce":"$undefined"}] c:["$","script","script-6",{"src":"/_next/static/immutable/chunks/06f0haa4q81t6.js","async":true,"nonce":"$undefined"}] d:["$","script","script-7",{"src":"/_next/static/immutable/chunks/0kbnvbl7eptep.js","async":true,"nonce":"$undefined"}] e:["$","script","script-8",{"src":"/_next/static/immutable/chunks/3brmn4mcym1z7.js","async":true,"nonce":"$undefined"}] f:["$","script","script-9",{"src":"/_next/static/immutable/chunks/0_ln2_6lkmx32.js","async":true,"nonce":"$undefined"}] 10:["$","script","script-10",{"src":"/_next/static/immutable/chunks/2tvds67b366ea.js","async":true,"nonce":"$undefined"}] 11:["$","script","script-11",{"src":"/_next/static/immutable/chunks/442lhk44e6ykq.js","async":true,"nonce":"$undefined"}] 12:["$","script","script-12",{"src":"/_next/static/immutable/chunks/3b6wkamawtv3r.js","async":true,"nonce":"$undefined"}] 13:["$","script","script-13",{"src":"/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","async":true,"nonce":"$undefined"}] 14:["$","script","script-14",{"src":"/_next/static/immutable/chunks/3b0fdgj_zftzq.js","async":true,"nonce":"$undefined"}] 15:["$","script","script-15",{"src":"/_next/static/immutable/chunks/27ei9vnzeiq85.js","async":true,"nonce":"$undefined"}] 16:["$","script","script-16",{"src":"/_next/static/immutable/chunks/014aoh0qn81eo.js","async":true,"nonce":"$undefined"}] 17:["$","script","script-17",{"src":"/_next/static/immutable/chunks/1c00lzvzs706d.js","async":true,"nonce":"$undefined"}] 18:["$","script","script-18",{"src":"/_next/static/immutable/chunks/3ywgyv40llk3m.js","async":true,"nonce":"$undefined"}] 19:["$","script","script-19",{"src":"/_next/static/immutable/chunks/058g38eq00elg.js","async":true,"nonce":"$undefined"}] 1a:["$","script","script-20",{"src":"/_next/static/immutable/chunks/1rug2kwvfis1u.js","async":true,"nonce":"$undefined"}] 1b:["$","script","script-21",{"src":"/_next/static/immutable/chunks/21b3i3nowssv-.js","async":true,"nonce":"$undefined"}] 1c:["$","$L2f",null,{"children":["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]}] 1d:["$","$1","c",{"children":[null,["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}] 1e:["$","$1","c",{"children":[null,["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}] 1f:["$","$1","c",{"children":[null,["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}] 20:["$","$1","c",{"children":[null,["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}] 21:["$","$1","c",{"children":[null,["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$u36:od4,ndefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}] 36:o5fb,22:["$","$1","c",{"children":[["$","div",null,{"className":"flex","children":["$","$6",null,{"fallback":null,"children":"$L30"}]}],[["$","script","script-0",{"src":"/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","async":true,"nonce":"$undefined"}],["$","script","script-1",{"src":"/_next/static/immutable/chunks/2zves0p1ggtcw.js","async":true,"nonce":"$undefined"}],["$","script","script-2",{"src":"/_next/static/immutable/chunks/3cpp7c7yc-8su.js","async":true,"nonce":"$undefined"}],["$","script","script-3",{"src":"/_next/static/immutable/chunks/1l-5amv9gm5ec.js","async":true,"nonce":"$undefined"}],["$","script","script-4",{"src":"/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","async":true,"nonce":"$undefined"}],["$","script","script-5",{"src":"/_next/static/immutable/chunks/36ofm1pm6eeme.js","async":true,"nonce":"$undefined"}],["$","script","script-6",{"src":"/_next/static/immutable/chunks/05s1116x2xxgz.js","async":true,"nonce":"$undefined"}],["$","script","script-7",{"src":"/_next/static/immutable/chunks/34f45g3k3ibf_.js","async":true,"nonce":"$undefined"}],["$","script","script-8",{"src":"/_next/static/immutable/chunks/1uw8afofehcs7.js","async":true,"nonce":"$undefined"}],["$","script","script-9",{"src":"/_next/static/immutable/chunks/3wms78zzv6zr5.js","async":true,"nonce":"$undefined"}],["$","script","script-10",{"src":"/_next/static/immutable/chunks/3s93rqpoi-ptk.js","async":true,"nonce":"$undefined"}]],["$","$L31",null,{"children":["$","$6",null,{"name":"Next.MetadataOutlet","children":"$@32"}]}]]}] 36:ofa,29:["$","$1","h",{"children":[null,["$","$L33","sbCw7vvu4kJlS-aKQEPgfv",{"children":"$L34"}],["$","div","sbCw7vvu4kJlS-aKQEPgfm",{"hidden":true,"children":["$","$L35",null,{"children":["$","$6",null,{"name":"Next.Metadata","children":"$L36"}]}]}]]}] 36:o9e8,38:I[992579,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js"],""] 23:T1,?24:C 2a:T1,?2b:T6,locale2c:300 37:T4f9,(function(c){var d=document.documentElement,t=c.defaultTheme,s;try{s=localStorage.getItem(c.storageKey)}catch(e){}if(s)t=s;if(t==="system"){try{t=window.matchMedia("(prefers-color-scheme: dark)").matches?"dark":"light"}catch(e){t="light"}}d.classList.remove(...c.concreteThemes);d.classList.add(t);d.style.colorScheme=c.appearances[t]==="dark"?"dark":"light"})({"appearances":{"light":"light","dark":"dark","system":"dynamic","darkmatter":"light","bean":"light","bubblegum":"light","caffeine":"light","claude":"light","cosmic":"light","cute":"light","dreamy":"light","ghibli":"light","luxury":"light","matcha":"light","nature":"light","neo":"light","notebook":"light","pacman":"light","perpetuity":"light","pinky":"light","popsicle":"light","retro":"light","shell":"light","solar":"light","sunset":"light","tangerine":"light","tokyo":"light","tree":"light","twitter":"light","vintage":"light","windy":"light","zelda":"light"},"concreteThemes":["light","dark","darkmatter","bean","bubblegum","caffeine","claude","cosmic","cute","dreamy","ghibli","luxury","matcha","nature","neo","notebook","pacman","perpetuity","pinky","popsicle","retro","shell","solar","sunset","tangerine","tokyo","tree","twitter","vintage","windy","zelda"],"defaultTheme":"system","storageKey":"theme"})4:["$","html",null,{"className":"geistsans_d5a4f12f-module__k4621G__variable geistmono_157ca88a-module__653Maq__variable geistpixelsquare_cf225766-module__bDjfTG__variable geistpixelgrid_6ebff038-module__k4MEpG__variable geistpixelcircle_7ee616e3-module__VTcpVG__variable geistpixeltriangle_d08a9537-module__Ny263q__variable geistpixelline_d71857ef-module__Rg2LMa__variable amiri_2ebd54a7-module___9Ujya__variable touch-manipulation font-sans antialiased","lang":"en","suppressHydrationWarning":true,"children":[["$","head",null,{"children":["$","script",null,{"dangerouslySetInnerHTML":{"__html":"$37"},"id":"nakafa-theme-bootstrap","suppressHydrationWarning":true,"type":"text/javascript"}]}],["$","body",null,{"className":"relative","children":[null,["$","p",null,{"className":"sr-only","children":["For AI agents: use ",["$","$L38",null,{"href":"/llms.txt","children":"/llms.txt"}]," for the Nakafa content index."]}],"$L39","$L3a","$L3b"]}]]}] 36:o8e2,3c:T423,{"@context":"https://schema.org","@type":"EducationalOrganization","@id":"https://nakafa.com/#educational-organization","name":"Nakafa","legalName":"PT. Nakafa Tekno Kreatif","alternateName":"Nakafa: Free Lessons from K-12 to University","description":"Study math, science, computer science, AI, and exam prep on Nakafa. Free lessons from K-12 to university with practice questions and explanations.","logo":"https://nakafa.com/logo.svg","image":"https://nakafa.com/logo.svg","url":"https://nakafa.com","sameAs":["https://twitter.com/nabilfatih_","https://www.linkedin.com/company/nakafa","https://www.instagram.com/nakafa.ai/","https://github.com/nakafaai","https://www.youtube.com/@nakafaa"],"email":"contact@nakafa.com","foundingDate":"2021","founder":{"@type":"Person","name":"Nabil Akbarazzima Fatih","url":"https://nakafa.com/en/contributor"},"areaServed":"Indonesia","knowsAbout":["Education","Mathematics","Science","Computer Science","Artificial Intelligence","K-12 Education","University Level Education","Online Learning","Educational Technology"]}39:["$","script",null,{"dangerouslySetInnerHTML":{"__html":"$3c"},"id":"json-ld-luo25f","type":"application/ld+json"}] 3a:["$","script",null,{"dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"WebSite\",\"@id\":\"https://nakafa.com/#website\",\"url\":\"https://nakafa.com\",\"name\":\"Nakafa\",\"alternateName\":\"Nakafa: Free Lessons from K-12 to University\",\"description\":\"Study math, science, computer science, AI, and exam prep on Nakafa. Free lessons from K-12 to university with practice questions and explanations.\",\"publisher\":{\"@type\":\"Organization\",\"name\":\"Nakafa\",\"legalName\":\"PT. Nakafa Tekno Kreatif\",\"logo\":\"https://nakafa.com/logo.svg\",\"url\":\"https://nakafa.com\"},\"maintainer\":{\"@type\":\"Organization\",\"name\":\"Nakafa\",\"legalName\":\"PT. Nakafa Tekno Kreatif\",\"logo\":\"https://nakafa.com/logo.svg\",\"url\":\"https://nakafa.com\"},\"inLanguage\":\"en\",\"potentialAction\":{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https://nakafa.com/search?q={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}}"},"id":"json-ld-9vmosf","type":"application/ld+json"}] 36:o113,3d:I[912310,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js"],"default"] 36:obd73,3b:["$","$L3d",null,{"formats":"$undefined","locale":"en","messages":{"Metadata":{"title":"Nakafa: Free Lessons from K-12 to University","description":"Study math, science, computer science, AI, and exam prep on Nakafa. Free lessons from K-12 to university with practice questions and explanations.","short-description":"Free lessons for K-12 through university.","very-short-description":"Free learning materials.","keywords":"free lessons, math lessons, physics lessons, chemistry lessons, biology lessons, computer science lessons, AI lessons, data science lessons, practice questions, worked solutions, exam prep, online try out, K-12 materials, university materials, open education, Nakafa","classification":"Education"},"Common":{"copyright":"Copyright © {year} PT. Nakafa Tekno Kreatif. All rights reserved.","made-with-love":"Made with love","version":"Version {version}","beta":"Beta","about":"About","theme":"Theme","light":"Light","dark":"Dark","system":"System","darkmatter":"Darkmatter","sunset":"Sunset","nature":"Nature","bean":"Bean","bubblegum":"Bubblegum","caffeine":"Caffeine","cute":"Cute","claude":"Claude","cosmic":"Cosmic","luxury":"Luxury","shell":"Shell","solar":"Solar","ghibli":"Ghibli","tree":"Tree","tokyo":"Tokyo","neo":"Neo","perpetuity":"Perpetuity","pinky":"Pinky","popsicle":"Popsicle","retro":"Retro","tangerine":"Tangerine","twitter":"Twitter","notebook":"Notebook","dreamy":"Dreamy","windy":"Windy","matcha":"Matcha","zelda":"Zelda","pacman":"Pacman","study":"Study","vintage":"Vintage","home":"Home","source":"Source","source-code":"Source code","language":"Language","articles":"Articles","material":"Material","subject":"Subjects","for-you":"For you","explore":"Explore","references":"References","show":"Show","hide":"Hide","no-website":"No website","high":"High","official":"Official","content":"Content","on-this-page":"On this page","bibliography":"Bibliography","videos":"Videos","previous":"Previous","next":"Next","undefined":"Undefined","radian":"Radian","share":"Share","share-copied":"Link copied!","contributor":"Contributor","search":"Search","select":"Select","navigate":"Navigate","close":"Close","community":"Community","report":"Report","copy-markdown":"Copy Markdown","copy-content":"Copy Content","copy":"Copy","copy-success":"Copied!","copy-error":"Couldn't copy","open":"Open","open-in-github":"Open in GitHub","open-in-chatgpt":"Open in ChatGPT","open-in-claude":"Open in Claude","open-in-t3-chat":"Open in T3 Chat","open-in-gemini":"Open in Gemini","see-on-youtube":"See on YouTube","subscribe":"Subscribe","comments":"Comments","anonymous":"Anonymous","delete":"Delete","edit":"Edit","move-up":"Move Up","move-down":"Move Down","more-actions":"More actions","reply":"Reply","replying-to-user":"Replying to ","new-messages":"{count, plural, =1 {# new message} other {# new messages}}","left-off-here":"You left off here","cancel":"Cancel","like":"Like","dislike":"Dislike","former-official":"Former Official","see":"See","chat":"Chat","no-chats":"No chats yet.","exercises":"Exercises","try-out":"Try out","try-out-short":"Tryout","search-country-placeholder":"Search country...","no-country-found":"No country found.","reaction":"Reaction","reacted-by":"{names}","reacted-by-more":"{names} and {count} more","emoji-picker-placeholder":"Select an emoji...","no-emoji-found":"No emoji found.","customize":"Customize","back-to-latest":"Back to latest","back":"Back"},"LearningPrograms":{"metadata-title":"Start learning with Nakafa","metadata-description":"Choose what you need help with and one first step.","curriculum-index-metadata-title":"School curricula on Nakafa","curriculum-index-metadata-description":"Choose a school curriculum pathway and browse Nakafa subjects by country-aligned standards.","curriculum-index-title":"School curricula","preference-save-error":"We could not save your curriculum preference.","plan-item-untitled":"Learning step","program-status":{"hidden":"Hidden","planned":"Soon","partial":"Partly ready","available":"Ready","archived":"Archived"},"onboarding":{"role-title":"How will you use Nakafa?","role":{"student":{"title":"Student","description":"Learn, practice, and tutor."},"teacher":{"title":"Teacher","description":"Prepare lessons for class."},"parent":{"title":"Parent","description":"Help your child learn simply."}},"focus":{"student":{"title":"What do you want to focus on?","school":{"title":"School lessons","description":"Read clear explanations."},"exam":{"title":"University entrance","description":"Practice before an exam."}},"teacher":{"title":"What do you want to prepare?","materials":{"title":"Teaching materials","description":"Prepare explanations for class."},"practice":{"title":"Student practice","description":"Prepare practice questions."}},"parent":{"title":"What does your child need help with?","understand":{"title":"Understand lessons","description":"Read simple explanations."},"practice":{"title":"Practice questions","description":"Prepare practice before an exam."}}},"back":"Back","continue":"Continue","save-cta":"Start learning","invalid-selection":"Choose your role and one learning focus.","save-error":"We could not save your choice. Try again.","unavailable-title":"Choose another option for now","unavailable-helper":"This choice is not ready yet.","auth-title":"Sign in to start","auth-helper":"Save your first plan and continue on any device.","auth-cta":"Sign in to Nakafa"},"kind":{"school-curriculum":"Curriculum","assessment":"Practice questions","admission-exam":"Admission exam","custom-program":"Custom program","institution-program":"Institution program"},"interest":{"school-curriculum":{"title":"School lessons"},"exam-prep":{"title":"University entrance"},"assessment-prep":{"title":"Practice questions"}},"plan-item-status":{"ready":"Ready","done":"Done","skipped":"Skipped"}},"Comments":{"add-comment-placeholder":"Add a comment...","comment":"Comment","no-comments":"No comments yet."},"Subject":{"elementary-school":"Elementary School","middle-school":"Middle School","high-school":"High School","vocational-school":"Vocational School","university":"University","grade":"Grade {grade}","grade-description":"Choose the subject that matches your grade.","subject-description":"Choose a grade, then open the topic you want to study.","chapter":"Chapter","mathematics":"Mathematics","physics":"Physics","chemistry":"Chemistry","biology":"Biology","geography":"Geography","history":"History","economy":"Economy","sociology":"Sociology","literature":"Literature","informatics":"Informatics","geospatial":"Geospatial","game-engineering":"Game Engineering","ai-ds":"Artificial Intelligence & Data Science","computer-science":"Computer Science","technology-electro-medical":"Technology Electro-Medical","political-science":"Political Science","informatics-engineering":"Informatics Engineering","international-relations":"International Relations","bachelor":"Bachelor","master":"Master","phd":"PhD","learn-with-nakafa":"Learn with Nakafa"},"Articles":{"description":"Read educational articles with clear context, data, and references.","politics":"Politics","official":"Official","official-description":"Made by Nakafa","contributor":"Contributor","contributor-description":"Made by contributor","articles":"Articles","read-article-on-nakafa":"Read article on Nakafa"},"Holy":{"holy":"Holy","quran":"Quran","quran-description":"Read the Quran with verse-by-verse translation.","verse":"Verse","verse-count":"Verse {count}","interpretation":"Interpretation","surah-title":"Surah {number}: {name} ({translation}) - {quran}","verses":"verses","read-quran-description":"Read the Quran online with verse-by-verse translation and tafsir on Nakafa"},"Exercises":{"exercises":"Exercises","answer":"Answer","correct":"Correct","incorrect":"Incorrect","score":"Score","reset":"Reset","explanation":"Explanation","number-count":"Number {count}","route-question-title":"{set} Question {number}","program-domain-list-description":"Choose an available practice domain to open question sets.","domain-set-list-description":"Choose an available practice set to open the questions for this domain.","high-school":"High School","middle-school":"Middle School","grade-9":"Grade 9","tka":"TKA","snbt":"SNBT","type-description":"Practice questions with explanations to check your understanding.","mathematics":"Mathematics","quantitative-knowledge":"Quantitative Knowledge","mathematical-reasoning":"Mathematical Reasoning","general-reasoning":"General Reasoning","indonesian-language":"Indonesian Language","english-language":"English Language","general-knowledge":"General Knowledge and Understanding","reading-and-writing-skills":"Reading and Writing Skills","simulation":"Simulation","simulation-description":"Work in exam mode. Results and explanations appear after submission.","practice":"Practice","practice-description":"Work at your own pace, then check the answer and explanation.","start":"Start","start-exercise-title":"Start exercise","start-exercise-description":"Choose between simulation or practice mode to start your exercise.","start-exercise-error":"Couldn't start the exercise. Please try again.","start-exercise-success":"Good luck with the exercise!","complete":"Complete","complete-exercise-title":"Finish exercise","complete-exercise-description":"Review your answers one last time before submitting to see your score.","complete-exercise-stats":"You have answered {answered} out of {total} questions.","complete-exercise-error":"Something went wrong finishing the exercise.","time-limit-label":"Time limit","time-limit-placeholder":"Select time limit","time":"Time","answered":"Answered","attempt-not-in-progress":"Please start a new session to continue practicing.","attempt-not-found":"Please start the exercise first.","submit-answer-error":"We couldn't save your answer. Please try again.","practice-exercises":"Practice exercises to understand the material"},"Tryouts":{"title":"What tryout do you want today?","metadata-description":"Choose a country, exam, and tryout set from Nakafa.","country-selector-label":"Country","exam-selector-label":"Exam","country-count":"{count, plural, =0 {No countries yet} =1 {# country} other {# countries}}","exam-count":"{count, plural, =0 {No exams yet} =1 {# exam} other {# exams}}","set-count":"{count, plural, =0 {No sets yet} =1 {# set} other {# sets}}","open-country-cta":"Open country","open-exam-cta":"Open exam","open-set-cta":"Open set","open-section-cta":"Open section","back-to-tryout":"Back to tryout","back-to-country":"Back to country","back-to-exam":"Back to exam","back-to-set":"Back to set","list-empty":"There are no tryouts showing right now.","preference-save-error":"We could not save your tryout preference yet.","scoring-irt":"IRT scoring","scoring-raw":"Raw scoring","scoring-weighted":"Weighted scoring","start-cta":"Start tryout","restart-cta":"Start again","free-cta":"Start free","start-pro-cta":"Start with Pro","restart-pro-cta":"Start again with Pro","continue-cta":"Continue","cancel-cta":"Not yet","start-dialog-title":"Start this tryout?","start-dialog-description":"Your tryout stays active for up to 3 days, while your access remains active. Once you start, you can choose which section to do first.","free-dialog-title":"Try 1 tryout for free","free-dialog-description":"You get 1 complete tryout for free. It is used only after the tryout starts successfully and stays active for 3 days.","free-entry-dialog-description":"You get 1 complete tryout for free. It is used only after this tryout starts successfully. This set's timer starts immediately.","restart-dialog-title":"Start this tryout from the beginning?","restart-dialog-description":"You will start over. Your previous result stays saved.","restart-entry-dialog-description":"You will start over, and this set's timer starts immediately. Your previous result stays saved.","start-success":"Tryout started. You can choose which section to work on first.","start-entry-dialog-description":"This set's timer starts as soon as you begin.","start-entry-success":"Tryout started. The timer is now running.","paywall-title":"Your next tryout needs Nakafa Pro","paywall-description":"You have used your free tryout.","paywall-benefit-access":"Start other tryout sets and repeat tryouts while Pro is active.","paywall-benefit-feedback":"Get IRT scoring on supported sets and detailed explanations.","checkout-cta":"See Pro pricing","checkout-error":"We could not open Pro checkout. Please try again.","start-error":"We could not start the tryout yet. Please try again.","start-not-ready-error":"This tryout is not ready to open yet.","start-unavailable-error":"This tryout is no longer available.","score-label-irt":"IRT score","score-label-standard":"Score","correct-answers-label":"Correct answers","score-status-estimated":"Preliminary","score-status-verified-irt":"IRT Verified","score-status-official":"Official","score-card-review-hint":"Open each section to review answers and explanations.","attempt-menu-label":"History","attempt-menu-search-placeholder":"Search attempts...","attempt-menu-empty":"No matching attempts found.","attempt-select-label":"Attempt {number}","entry-head-ready":"This set is ready whenever you want to start.","part-head-needs-tryout":"Start the tryout first to choose any section to work on.","part-head-ready":"This section is ready whenever you want to start it while the tryout is still active.","part-head-in-progress":"You're currently working on this section.","part-head-expiring":"Time is up. Your answers are being saved.","part-head-completed":"This section is done, please check the answers and explanations below.","part-head-completed-pending-review":"This section is done, but explanations will open after the whole tryout finishes.","part-head-completed-time-expired":"Time is up and answers auto-submitted, please check the explanations below.","part-head-completed-time-expired-pending-review":"Time is up and answers auto-submitted, but explanations will open after the tryout finishes.","part-head-ended":"The tryout is finished, open this section to review the questions and explanations.","part-questions-label":"Questions","part-time-label":"Time","set-column-name":"Name","set-column-questions":"Questions","set-column-score":"Score","set-column-status":"Status","set-sort-label":"Sort {column}","set-sort-name-ascending":"A to Z","set-sort-name-descending":"Z to A","set-sort-questions-ascending":"Fewest","set-sort-questions-descending":"Most","set-sort-score-ascending":"Lowest score","set-sort-score-descending":"Highest score","set-filter-label":"Filter {column}","set-filter-all":"All","status-not-started":"Not started","status-in-progress":"In progress","status-completed":"Completed","status-expired":"Time expired","remaining-time-label":"Time left","time-hours-short":"hr","time-minutes-short":"min","time-seconds-short":"sec","start-part-cta":"Start section","start-part-success":"Section started. The timer is now running.","start-part-error":"We could not start this section yet. Please try again.","complete-part-cta":"Finish section","complete-part-title":"Finish this section?","complete-part-description":"If you finish now, the answers in this section will be locked.","complete-part-success":"Section finished. You can choose another section or go back to the set.","complete-part-error":"We could not finish this section yet. Please try again.","back-to-set-cta":"Back to set","slug-description":"When you're ready, start this tryout and choose which section you want to do first.","question-unit":"questions"},"Utils":{"search":"Search","clear-search":"Clear search","search-bar-placeholder":"Search content...","search-placeholder":"Find what you want...","search-not-found":"We couldn't find anything matching that.","search-loading":"Finding results...","search-help":"Type to start searching...","search-error":"An error occurred while searching.","search-title":"Search Learning Materials","search-description":"Search free learning materials, educational articles, practice exercises, and study resources. Find the topic you are studying."},"Home":{"greeting":"Hi, {name}","title":"What do you want to learn?","contribute":"Contribute","videos":"Videos","trending-subjects":"Trending Subjects This Week","views":"{count} views","explore-materials":"Explore Materials","guest":"you","continue-learning":"Continue Learning","continue-learning-description":"Continue reading where you left off","no-recent-views":"No reading history yet","no-recent-views-description":"Start exploring available learning materials!","start-learning":"Start Learning"},"Marketing":{"about":"About","features":"Features","pricing":"Pricing","sign-in":"Sign in","sign-up":"Sign up","try-nakafa":"Try Nakafa"},"Weather":{"loading":"Loading weather...","error":"Couldn't load weather data","unknown-location":"Unknown Location","unknown-country":"Unknown Country","high":"H","low":"L"},"Videos":{"discover":"Discover videos"},"NotFound":{"title":"Page Not Found","description":"Oops! That page doesn't exist or isn't ready yet.","home-button":"Home","contribute-button":"Contribute"},"Error":{"title":"Oops, something went wrong!","description":"Please help us by reporting this on GitHub.","retry":"Retry","report":"Report"},"Contributor":{"title":"Contributor","description":"Meet the people who made Nakafa possible."},"ComingSoon":{"title":"Coming Soon","description":"This feature is not available yet. Please check back later or contribute to the project.","contribute":"Contribute"},"Auth":{"continue-with-google":"Continue with Google","logout":"Logout","login":"Login","login-cta-title":"Log in","login-cta-action":"Free Nakafa account","account":"Account","settings":"Settings","settings-description":"Manage your Nakafa account settings, preferences, and profile information to personalize your learning experience.","profile":"Profile","profile-description":"View user learning profiles with educational contributions, comments, study progress, and community activity.","chat":"Chat","chat-description":"Use the AI learning assistant for homework help, concept explanations, and study conversations.","subscriptions":"Subscriptions","subscriptions-description":"Manage Nakafa Pro, 3,000 monthly AI credits, and your payment portal.","get-pro":"Get Pro","manage":"Manage","plan-free":"Free","plan-pro":"Pro","name":"Name","name-description":"This name will appear on your profile and comments.","name-footer":"Please use between 3 and 32 characters.","name-placeholder":"Enter your name...","role":"Role","role-description":"Your role helps us tailor your learning experience.","role-footer":"You can change your role anytime.","role-placeholder":"Select a role","curriculum":"Curriculum","curriculum-description":"Your curriculum preference keeps subject shortcuts aligned with the pathway you use most.","curriculum-footer":"You can change your curriculum anytime.","curriculum-placeholder":"Select a curriculum","delete-account":"Delete account","delete-account-description":"Permanently delete your profile and personal data from Nakafa.","delete-account-footer":"This action cannot be undone.","delete-account-dialog-title":"Delete account?","delete-account-dialog-description":"Your profile and personal data will be permanently deleted. Active subscriptions will be canceled, Nakafa Pro will end, and schools you created will pass to another active member.","delete-account-session-expired":"This session is too old. Sign in again to continue.","delete-account-school-member-required":"Add one active member to each school you created, then try again.","delete-account-error":"We could not delete your account. Wait a moment, then try again.","delete-account-sign-in-again":"Sign in again","teacher":"Teacher","student":"Student","parent":"Parent","administrator":"Administrator","save":"Save","developers":"Developers","developers-description":"Access developer tools, API keys, and integration resources to build applications with Nakafa's educational content and services.","api-key":"API Key","api-key-description":"Manage your API keys to authenticate with Nakafa API.","api-key-footer":"Create a new API key here.","api-key-confirmation-description":"Keep your API key safe and secure.","new-api-key":"New API Key","api-key-created":"API key created!","no-api-keys":"No API keys found.","create":"Create","api-key-name":"API Key Name","api-key-name-placeholder":"Enter your API key name...","expires-in":"Expires in","expires-in-placeholder":"Days until expiration...","7-days":"7 days","30-days":"30 days","90-days":"90 days","180-days":"180 days","365-days":"365 days","never":"Never","expires":"Expires","api-key-copied":"API key copied!","delete-api-key":"Delete API Key","delete-api-key-description":"Are you sure? This action cannot be undone.","delete":"Delete","api-key-deleted":"API key deleted."},"EventAccess":{"title":"Partner event access","unavailable-invalid-code":"This event link is invalid or no longer available.","unavailable-disabled":"This event access is temporarily disabled.","unavailable-not-started":"This event access is not open yet. Please try again later.","unavailable-ended":"This event access has ended.","sign-in-description":"Sign in to claim access.","ready-description":"Activate to start.","active-until":"Active until {date}","ended-at":"Ended {date}","sign-in-cta":"Continue","redeem-cta":"Activate","already-active-cta":"Already active","view-tryout-cta":"View","redeem-success":"Event access is active until {date}.","redeem-error":"We could not activate this event access yet. Please try again."},"Ai":{"ask-nina":"Ask Nina","text-placeholder":"Ask Nina anything...","error-message":"Oops, something went wrong. Try switching the AI model.","insufficient-credits":"You are out of AI credits. Wait for the next credit reset or upgrade to Pro for 3,000 monthly credits.","retry":"Retry","rate-limit-message":"Whoa, slow down! Please try again in a moment.","nakafa":"Nakafa","nakafa-search":"Nakafa results","nakafa-search-results":"Content found","nakafa-search-articles":"Articles found","nakafa-search-subject":"Materials found","nakafa-search-tryout":"Try-outs found","nakafa-search-quran":"Verses found","nakafa-search-empty":"No matching content found.","nakafa-content":"Material","nakafa-exercise":"Exercises","nakafa-quran":"Quran","nakafa-quran-verse-count":"{count, plural, one {# verse} other {# verses}}","question-number":"Question {number}","nakafa-loading":"Reading {kind}...","nakafa-error":"Couldn't read {kind}.","math-apart":"Splitting fractions","math-cancel":"Cancelling factors","math-circle":"Finding circle","math-combination":"Counting combinations","math-compare":"Comparing","math-cumulative_probability":"Finding cumulative probability","math-determinant":"Finding determinant","math-differentiate":"Differentiating","math-distance":"Measuring distance","math-distribution":"Checking distribution","math-domain":"Finding domain","math-eigen_analysis":"Analyzing eigenstructure","math-eigenvalues":"Finding eigenvalues","math-eigenvectors":"Finding eigenvectors","math-evaluate":"Calculating","math-expected_value":"Finding expectation","math-expand":"Expanding","math-factor":"Factoring","math-gcd":"Finding GCD","math-integrate":"Integrating","math-intersection":"Finding intersection","math-inverse":"Finding inverse","math-interval_probability":"Finding interval probability","math-is_prime":"Checking prime","math-lcm":"Finding LCM","math-limit":"Finding limit","math-line":"Finding line","math-linear_system":"Solving system","math-matrix_multiply":"Multiplying matrices","math-mean":"Finding mean","math-median":"Finding median","math-midpoint":"Finding midpoint","math-mode":"Finding mode","math-modular":"Finding remainder","math-permutation":"Counting permutations","math-point_probability":"Finding probability","math-prime_factorization":"Factoring primes","math-product":"Multiplying series","math-quartiles":"Finding quartiles","math-rank":"Finding rank","math-rationalize":"Rationalizing","math-roots":"Finding roots","math-rref":"Reducing matrix","math-series":"Expanding series","math-simplify":"Simplifying","math-slope":"Finding slope","math-solve":"Solving","math-standard_deviation":"Finding deviation","math-summation":"Summing series","math-tail_probability":"Finding tail probability","math-together":"Combining fractions","math-variance":"Finding variance","math-variance_probability":"Finding variance","math-z_score":"Finding z-score","math-error":"This part could not be checked. Write the math expression or data more completely.","math-loading":"Working on calculation...","math-step":"Step {number}","math-relation-differentiate":"has derivative","math-relation-limit":"has limit","math-relation-solve":"has solution","math-compare-verified":"same as","math-compare-contradicted":"different from","math-compare-inconclusive":"not proven same as","math-input":"Given","math-condition":"Condition","math-item-algebraic-multiplicity":"Algebraic multiplicity","math-item-counterexample":"Counterexample","math-item-diagonalizable":"Diagonalizable","math-item-domain":"Domain","math-item-eigenbasis":"Eigenspace basis","math-item-eigenvalue":"Eigenvalue","math-item-eigenvector":"Eigenvector","math-item-factor":"Factor","math-item-geometric-multiplicity":"Geometric multiplicity","math-item-mode":"Mode","math-item-approximation":"Approximation","math-item-q1":"Lower quartile","math-item-q2":"Median","math-item-q3":"Upper quartile","math-item-result":"Result","math-item-root":"Root","math-item-singularity":"Problem point","math-item-solution":"Solution","math-item-status":"Conclusion","math-value-divergent":"Divergent","math-value-no":"No","math-value-yes":"Yes","thinking":"Thinking...","thought-for":"Thought for {duration} seconds","thought-for-a-few-seconds":"Thought for a few seconds","follow-up":"Follow up","copy-message":"Copy message","retry-message":"Retry message","see":"See","scrape":"Scrape","scrape-loading":"Reading source...","scrape-done":"Source read","scrape-error":"Couldn't read source.","web-search":"Web search","web-search-loading":"Looking for info...","web-search-error":"Couldn't find any info.","web-search-empty":"No sources returned.","model":"Model","model-subtitle-nakafa-lite":"Everyday learning","model-subtitle-nakafa-pro":"Deep reasoning","show-more":"Show more","show-less":"Show less","new-chat-title":"What do you want to learn?","new-chat-description":"Just ask me, don't hesitate!","suggestion-current-material":"this material","suggestion-explain":"Explain this","suggestion-explain-prompt":"Explain {title} in simple student-friendly language.","suggestion-example":"Show example problem","suggestion-example-prompt":"Give me an example problem about {title} with a step-by-step solution.","suggestion-summary":"Get key points","suggestion-summary-prompt":"Summarize {title} into the key ideas I need to remember.","new-chat":"New chat","chats":"Chats","search-chats":"Search your chats...","rename-chat":"Rename chat","delete-chat":"Delete chat","delete-chat-description":"Are you sure? This chat cannot be recovered once deleted.","confirm":"Confirm","share-chat":"Share chat","share-chat-description":"Be careful when sharing this link with strangers.","private":"Private","private-description":"Only you can view the chat.","public":"Public","public-description":"Everyone can view the chat.","create-link":"Create link","copy-link":"Copy link","link-copied":"Link copied!","private-chat-error":"Access denied","private-chat-error-description":"This isn't your chat. Ask the owner for access.","credits-label":"Credits","token-usage":"Token Usage","input-tokens":"Input","output-tokens":"Output","total-tokens":"Total","recent-chats":"Recent Chats","speed":"Playback speed"},"Pricing":{"headline":"We were students too. We know what it is like to choose between learning and eating. Core access is free. Always.","free-title":"Free","free-description":"Start learning at your own pace","free-feature-1":"Access to 5,000+ lessons","free-feature-2":"2,000+ practice exercises with explanations","free-feature-3":"Basic AI tutor (10 messages per day)","free-feature-4":"1 complete tryout for free","free-feature-5":"Community access on Discord","free-cta":"Start Learning","pro-title":"Pro","pro-description":"Practice more seriously with Nina, 3,000 monthly AI credits, and repeat tryout access.","pro-period":"/month","pro-feature-1":"Everything in Free, plus:","pro-feature-2":"3,000 AI credits each month for premium Nina models","pro-feature-3":"Start another tryout set or repeat a tryout, with IRT scoring on supported sets and detailed explanations","pro-feature-4":"Download lessons as PDFs and listen to audio versions","pro-feature-5":"Priority support when you need guidance","pro-cta":"Get Pro"},"Faq":{"badge":"Support","headline":"Still have questions?","description":"Cannot find what you need? Reach out to us directly.","cta-contact":"Contact founder","q1":"Is Nakafa really free?","a1":"Yes. Core content and 1 complete tryout are free. Pro is required to start another tryout set or repeat a tryout, use premium AI models, get 3,000 monthly AI credits, and download PDFs. Basic learning materials stay free of paywalls.","q2":"What AI models can I use?","a2":"Everyone can use Nakafa Lite and Nakafa Pro. Credits decide how much you can use each model.","q3":"Can I download lessons for offline use?","a3":"PDF downloads are a Pro feature. You can save any lesson as a PDF to study offline or print. Free users can always access content online.","q4":"What subjects and grades do you cover?","a4":"We cover K-12 through university. Mathematics, Physics, Chemistry, Biology, Computer Science, and more. From elementary basics to advanced university courses.","q5":"Is my data private?","a5":"Yes. We do not sell your data. AI conversations are processed securely. You can delete your chat history anytime. We are privacy-first by design.","q6":"Can schools use Nakafa?","a6":"Absolutely. We offer custom solutions for classrooms and institutions. Contact founder for LMS integration, student management, and custom branding.","q7":"How does Nakafa ensure content accuracy?","a7":"All content is created by qualified contributors and reviewed by the community. Our source-available approach means anyone can inspect materials and propose improvements. Practice exercises include explanations so you learn from mistakes, not just scores."},"Features":{"story":"Learning doesn’t stop when you finish reading. Put it to the test with Tryout, see what still feels unclear, then ask Nina without starting over.","subjects-title":"Start with the subject you need","subjects-navigation":"Available subjects","tryout-title":"After learning, see what you really understood","nina-title":"If you are still unsure, Nina already knows which part you mean","nina-prompt":"For the operation $$\\triangle(a,b)=ka+\\frac{b}{m}$$, we know $$\\triangle(2,4)=8$$ and $$\\triangle(3,5)=11$$. How do I find $$\\triangle(5,9)$$?","nina-reasoning":"Compare the two known equations. Their difference reveals the positive integer values of $$k$$ and $$m$$ before the final calculation.","nina-answer":"Subtract the first equation from the second:\n\n$$k+\\frac{1}{m}=3$$\n\nBecause $$k$$ and $$m$$ are positive integers, $$\\frac{1}{m}$$ can only be an integer when $$m=1$$. That makes $$k=2$$.\n\nPut both values into the final operation:\n\n$$\\triangle(5,9)=5(2)+\\frac{9}{1}=19$$\n\nSo $$\\triangle(5,9)=19$$.","projectile-title":"Motion becomes easier to understand when you can see it for yourself","projectile-controls":"Choose a cannonball path","projectile-sixty-degree":"Sixty Degrees","projectile-long-drive":"Long Drive","projectile-high-arc":"High Arc","projectile-view-label":"Cannonball projectile analysis visual","projectile-horizontal-component":"Horizontal component","projectile-vertical-component":"Vertical component","projectile-peak-time":"Peak time","projectile-flight-time":"Flight time","projectile-range":"Range","projectile-instantaneous-velocity":"Velocity at two seconds"},"CurriculaSection":{"headline":"Your curriculum may differ. Your learning still stays connected.","description":"Start from your school pathway. Lessons, Tryout, and Nina follow the curriculum you use.","cta":"Explore all curricula","navigation":"Available curricula"},"SchoolsSection":{"badge":"For Schools","headline":"Every school has different needs. We get it.","description":"Need an LMS, content integration, or a custom classroom flow? Pick what works for your school.","cta":"Discuss your needs"},"TrustSection":{"headline":"You do not have to take our word for it. Follow the lesson back to its sources.","description":"Read the explanation, follow its references, or open the source when you want to check how it was built.","open-lesson":"Open this lesson","open-lesson-short":"Open lesson","open-source":"Open .md","human-label":"Human","agent-label":"Agent","comparison-slider-label":"Resize the human and agent views","lesson-preview-label":"Nakafa lesson view","source-preview-label":"Nakafa Markdown source","lesson-heading":"From Paper to Pandemic","lesson-opening-before-folds":"Have you ever imagined folding a sheet of paper","lesson-folds-math":"42 \\text{ times}","lesson-opening-after-folds":"? If it were possible to do so, its thickness would exceed the distance from Earth to the Moon! This is because each fold doubles the thickness of the paper, this is what we call","lesson-growth-term":"exponential growth","lesson-growth-before-year":"Exponential growth occurs when something increases by a constant multiplier in each time interval. In early","lesson-year-math":"2020","lesson-growth-after-year":", the world experienced a real example of exponential growth through the spread of the COVID-19 virus. One infected person could transmit to two people, then four, eight, and so on.","lesson-definition-heading":"Definition of Exponents","lesson-definition":"An exponent is a shorthand way to write repeated multiplication. Imagine you are calculating how many people are infected with a virus like COVID-19. At each transmission phase, the number of infected people will increase in an interesting pattern:","lesson-sequence-math":"1 = 2^0 \\quad 2 = 2^1 \\quad 4 = 2 \\times 2 = 2^2 \\quad 8 = 2 \\times 2 \\times 2 = 2^3 \\quad 16 = 2 \\times 2 \\times 2 \\times 2 = 2^4"},"About":{"meta-title":"Free Open Learning Materials from K-12 to University","title":"Learn until it clicks.","description":"Pick a subject, test what you know with Tryout, and ask Nina when you get stuck.","explore-subjects":"Explore subjects","try-tryout":"Try a Tryout","contribute":"Contribute","start-learning":"Start learning","join-community":"Join community","community-title":"Find people who get what you are learning","community-description":"Every lesson is made by someone who was confused too. Join our Discord to ask questions, share resources, or help others out.","curriculum-title":"Learn exactly what you need, when you need it","curriculum-description":"Pick your grade, choose a subject, or search for the topic you are studying. No endless scrolling.","company":"Company","community":"Community","about-us":"About Us","trusted-badge":"Learning together","trusted-headline":"Students from these schools and universities learn with Nakafa.","trusted-description":"They start with open lessons, then keep going at their own pace."},"File":{"exceeds-max-size":"{fileName} exceeds maximum size of {maxSizeFormatted}.","exceeds-max-size-multiple":"{fileName} exceeds maximum size of {maxSizeFormatted}.","not-accepted-file-type":"{fileName} is not an accepted file type.","max-files-exceeded":"Maximum of {maxFiles} files allowed.","some-files-exceed-max-size":"Some files exceed maximum size of {maxSizeFormatted}.","file-exceeds-max-size":"File exceeds maximum size of {maxSizeFormatted}.","unknown-file":"Unknown file","unknown-file-size":"Unknown file size"},"Legal":{"terms-and-policies":"Terms and Policies","terms-of-service":"Terms of Service","terms-of-service-description":"Read Nakafa's Terms of Service to understand the rules and guidelines for using our educational platform and services.","privacy-policy":"Privacy Policy","privacy-policy-description":"Learn how Nakafa collects, uses, and protects your personal data and privacy when using our learning platform.","security-policy":"Security Policy","security-policy-description":"Review Nakafa's security practices and policies to understand how we safeguard your data and ensure platform security.","legal-description":"By using our services, you agree to our Terms of Service and Privacy Policy."},"School":{"Common":{"home":"Home","learning":"Learning","classes":"Classes","nakafa-materials":"Nakafa Materials","yours":"For you","notifications":"Notifications"},"Classes":{"classes":"Classes","search-placeholder":"Search classes...","create-class":"Create class","create-class-description":"Set up a learning space for materials, assessments, and class discussions.","create":"Create","name-label":"Name","name-placeholder":"Class 10A","subject-label":"Subject","subject-placeholder":"Mathematics","year-label":"Academic Year","year-placeholder":"2024/2025","create-class-failed":"Couldn't create the class. Please try again.","no-classes-found":"No classes yet.","no-subjects-found":"No subjects found.","search-subjects-placeholder":"Search subjects...","join-class":"Join class","join-class-description":"Enter an invite code to access an existing class.","join":"Join","code":"Code","code-placeholder":"Enter the code...","join-class-failed":"Couldn't join the class. Please check the code and try again.","mathematics":"Mathematics","advanced-mathematics":"Advanced Mathematics","natural-science":"Natural Science","physics":"Physics","chemistry":"Chemistry","biology":"Biology","social-studies":"Social Studies","geography":"Geography","history":"History","economy":"Economy","sociology":"Sociology","civics":"Civics","informatics":"Informatics","geospatial":"Geospatial","computer-science":"Computer Science","ai-ds":"Artificial Intelligence & Data Science","game-engineering":"Game Engineering","informatics-engineering":"Informatics Engineering","technology-electro-medical":"Technology Electro-Medical","indonesian":"Indonesian Language","sundanese":"Sundanese","javanese":"Javanese","balinese":"Balinese","madurese":"Madurese","minangkabau":"Minangkabau","betawi":"Betawi","english":"English","literature":"Literature","arts":"Arts","music":"Music","crafts":"Crafts","physical-education":"Physical Education","health-education":"Health Education","islamic-education":"Islamic Education","christian-education":"Christian Education","catholic-education":"Catholic Education","hindu-education":"Hindu Education","buddhist-education":"Buddhist Education","confucian-education":"Confucian Education","political-science":"Political Science","international-relations":"International Relations","accounting":"Accounting","business":"Business","entrepreneurship":"Entrepreneurship","guidance-counseling":"Guidance & Counseling","people-search-placeholder":"Search people...","no-people-found":"No people found.","people":"People","forum":"Forum","assessments":"Assessments","assessments-search-placeholder":"Search assessments...","assessments-teacher-only":"Assessments will appear here once your teacher publishes them.","create-assessment":"Create assessment","create-assessment-description":"Build a practice set, assignment, quiz, exam, or tryout to track student progress.","edit-assessment-title":"Edit assessment","edit-assessment-description":"Update the title, description, mode, or schedule for this assessment.","assessment-created":"Assessment created.","assessment-updated":"Assessment updated.","assessment-deleted":"Assessment deleted.","delete-assessment-title":"Delete assessment?","delete-assessment-description":"This can't be undone.","create-assessment-failed":"Couldn't create the assessment. Please try again.","update-assessment-failed":"Couldn't update the assessment. Please try again.","delete-assessment-failed":"Couldn't delete the assessment. Please try again.","assessment-title-label":"Title","assessment-title-placeholder":"Midterm exam","assessment-description-label":"Description","assessment-description-placeholder":"Briefly describe what this assessment covers...","assessment-mode-label":"Mode","assessment-status-label":"Visibility","assessment-scheduled-at-label":"Schedule","assessment-scheduled-at-placeholder":"Choose date and time","assessment-scheduled-time-label":"Time","assessment-mode-practice":"Practice","assessment-mode-assignment":"Assignment","assessment-mode-quiz":"Quiz","assessment-mode-exam":"Exam","assessment-mode-tryout":"Try out","assessment-empty-description":"No description yet.","no-assessments-found":"No assessments yet.","material-items":"Materials","material-groups":"Folders","teacher":"Teacher","student":"Student","invite":"Invite","role":"Role","copy":"Copy","invite-teacher-title":"Invite Teacher","invite-teacher-description":"Share this code so teachers can join and help manage the class.","invite-student-title":"Invite Student","invite-student-description":"Share this code so students can join and start learning.","invite-code-copied":"Invite code copied to clipboard.","forum-search-placeholder":"Search forum...","no-forum-found":"No forum found.","new-forum":"New Forum","new-forum-title":"Start a Discussion","new-forum-description":"Share ideas, ask questions, or keep the class updated.","forum-panel-description":"Discuss anything with everyone in the class.","forum-title-label":"Discussion Title","forum-title-placeholder":"What's the topic?","forum-body-label":"Message","forum-body-placeholder":"Share your thoughts, questions, or announcements...","tag-label":"Category","tag-placeholder":"Select a category...","general":"General","question":"Question","announcement":"Announcement","assignment":"Assignment","resource":"Resource","create-forum-failed":"Failed to create forum. Please try again.","create-post-failed":"Failed to send message. Please try again.","unknown-user":"Unknown user","original-message-deleted":"Original message was deleted.","send-message-placeholder":"Send a message...","submit":"Submit","attachments":"Attachments","materials":"Materials","visibility-label":"Visibility","visibility-placeholder":"Select visibility...","public":"Public","private":"Private","emoji":"Emoji","failed-to-send-message":"Failed to send message.","failed-to-upload-file":"Failed to upload {fileName}.","modules-search-placeholder":"Search modules...","new-module":"New Module","new-module-title":"Create Module","new-module-description":"Group learning materials so students know where to start.","material-name-label":"Name","material-name-placeholder":"Introduction to Algebra","material-description-label":"Description","material-description-placeholder":"Briefly describe what this material covers...","material-status-label":"Visibility","status-draft":"Draft","status-published":"Published","status-schedule":"Scheduled","status-archived":"Archived","material-scheduled-at-label":"Schedule","material-scheduled-at-placeholder":"Select date and time","material-scheduled-time-label":"Time","create-material-group-failed":"Failed to create material. Please try again.","edit-material-title":"Edit Material","edit-material-description":"Update the module name, description, visibility, or schedule.","update-material-group-failed":"Failed to update material. Please try again.","material-deleted":"Material deleted.","delete-material-title":"Delete material?","delete-material-description":"This can't be undone.","delete-material-failed":"Couldn't delete the material. Please try again.","save":"Save","no-materials-found":"No materials found.","published":"Published","draft":"Draft","scheduled":"Scheduled","archived":"Archived"},"Onboarding":{"title":"Welcome to Nakafa School!","description":"Choose how your school will start using Nakafa School.","create":"Create a School","create-description":"For admins or school leaders setting up a learning space for their school.","join":"Join a School","join-description":"For teachers, students, or parents who already have a school invite code.","back":"Back","school-name":"School Name","school-name-placeholder":"SMA Negeri 1 Jakarta","school-email":"School Email","school-email-placeholder":"sma1@example.com","school-phone":"School Phone","school-phone-placeholder":"+62 123 456 7890","school-address":"School Address","school-address-placeholder":"Jl. Raya Jakarta No. 123","school-city":"School City","school-city-placeholder":"Jakarta","school-province":"School Province","school-province-placeholder":"DKI Jakarta","school-type":"School Type","school-type-placeholder":"Select a school type...","elementary-school":"Elementary School","middle-school":"Middle School","high-school":"High School","vocational-school":"Vocational School","university":"University","other":"Other","role":"I'm a","role-placeholder":"Select a role...","code":"Code","code-placeholder":"Enter the code...","teacher":"Teacher","student":"Student","parent":"Parent","school-creation-failed":"Failed to create school. Please try with a different email.","add-school":"Add school","schools":"Schools","search-school-placeholder":"Search schools...","no-schools-found":"No schools found.","school-joining-failed":"Failed to join school. Make sure the code is correct."}},"SEO":{"subject":{"title":"{title}: {chapter, select, __EMPTY__ {} other {{chapter} - }}{material} ({grade}) | Nakafa","description":"Learn {title} in {chapter, select, __EMPTY__ {} other {{chapter} }}{material} for {grade}. This page explains the concept, examples, and practice for checking understanding.","keywords":"{title}, {chapter, select, __EMPTY__ {} other {{chapter}, }}{material}, {grade}, learn, material, practice problems, exercises, education"},"exercise":{"title":"{number, select, 0 {} other {Question {number}{questionTotal, select, __EMPTY__ {} other {{questionTotal}}}: }}{set, select, __EMPTY__ {} other {{set}{number, select, 0 {: } other { - }}}}{group, select, __EMPTY__ {} other {{group} - }}{material} ({exam}) | Nakafa","description":"Take {material} {exam} exercise{group, select, __EMPTY__ {} other { {group}}}{set, select, __EMPTY__ {} other { {set}}} with {questionCount, plural, =0 {practice questions} =1 {1 question} other {{questionCount} questions}} and explanations for checking your reasoning.","keywords":"{material}, {exam}, {group, select, __EMPTY__ {} other {{group}, }}{set, select, __EMPTY__ {} other {{set}, }}exercise, practice questions, solutions, exam"},"exercise-program":{"title":"{exam} Practice Questions | Nakafa","description":"Choose {exam} practice domains for {category}. Each domain links to question sets with explanations for checking understanding.","keywords":"{exam}, {category}, practice questions, question sets, explanations, exam preparation"},"curriculum":{"title":"{title}{parent, select, __EMPTY__ {} other { - {parent}}}{program, select, __EMPTY__ {} other { ({program})}} | Nakafa","description":"Browse {title}{parent, select, __EMPTY__ {} other { in {parent}}}{program, select, __EMPTY__ {} other { for {program}}}. This curriculum index links learners to the relevant materials and practice routes.","keywords":"{title}, {parent, select, __EMPTY__ {} other {{parent}, }}{program, select, __EMPTY__ {} other {{program}, }}curriculum, learning path, materials, practice"},"article":{"title":"{title} - {category} | Nakafa","description":"Read {title} in {category}. This article presents context, data, and references readers can check.","keywords":"{title}, {category}, analysis, facts, latest, research, information, news"},"quran":{"title":"Surah {number}. {name} ({transliteration}) - {translation} | Nakafa","description":"Read Surah {name} ({transliteration}) with translation and tafsir. {numberOfVerses} verses from the Holy Quran.","keywords":"Surah {name}, Quran, {translation}, {revelation}, tafsir"}}},"now":"$undefined","timeZone":"UTC","children":["$L3e","$L3f"]}] 36:o7fd,40:I[685412,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js"],"MotionConfig"] 41:I[848317,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js"],"ThemeProvider"] 43:I[245596,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js"],"Toaster"] 44:I[741378,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js"],"Analytics"] 3e:[["$","$L40",null,{"reducedMotion":"user","children":["$","$L41",null,{"attribute":"class","defaultTheme":"system","disableTransitionOnChange":true,"enableSystem":true,"storageKey":"theme","themes":["light","dark","darkmatter","bean","bubblegum","caffeine","claude","cosmic","cute","dreamy","ghibli","luxury","matcha","nature","neo","notebook","pacman","perpetuity","pinky","popsicle","retro","shell","solar","sunset","tangerine","tokyo","tree","twitter","vintage","windy","zelda"],"children":[["$","div",null,{"className":"isolate","children":["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":["$L42",[]],"forbidden":"$undefined","unauthorized":"$undefined"}]}],["$","$L43",null,{}]]}]}],["$","$L44",null,{"debug":false,"mode":"production"}]] 3f:null 36:o147,45:I[884727,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0gk165nql56kf.js"],"Particles"] 36:o8e3,46:I[807002,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"default"] 36:o940,42:["$","div",null,{"className":"relative flex h-[calc(100svh-4rem)] items-center justify-center lg:h-svh","children":[["$","$L45",null,{"className":"pointer-events-none absolute inset-0 opacity-80"}],["$","div",null,{"className":"mx-6 rounded-xl border bg-card/30 p-6 shadow-sm backdrop-blur-xs","children":["$","div",null,{"className":"space-y-4 text-center","children":[["$","h1",null,{"className":"font-bold font-mono text-6xl text-destructive","children":"404"}],["$","div",null,{"className":"space-y-2","children":[["$","h2",null,{"className":"font-medium text-lg tracking-tight","children":"Page Not Found"}],["$","p",null,{"className":"mx-auto max-w-md text-muted-foreground text-sm","children":"Oops! That page doesn't exist or isn't ready yet."}]]}],["$","div",null,{"className":"mx-auto flex w-fit items-center gap-2","children":[["$","a",null,{"className":"inline-flex shrink-0 cursor-pointer select-none items-center justify-center gap-2 whitespace-nowrap rounded-md text-sm outline-none transition-all ease-out focus-visible:border-ring focus-visible:ring-[3px] focus-visible:ring-ring/50 active:not-aria-[haspopup]:translate-y-px disabled:pointer-events-none disabled:opacity-50 aria-invalid:border-destructive aria-invalid:ring-destructive/20 [&_svg:not([class*='size-'])]:size-4 [&_svg]:pointer-events-none [&_svg]:shrink-0 bg-secondary text-secondary-foreground shadow-xs hover:bg-[color-mix(in_oklch,var(--secondary)_99%,var(--background))] hover:shadow-md h-9 px-4 py-2 has-[>svg]:px-3","href":"https://github.com/nakafaai/nakafa.com","rel":"noopener noreferrer","target":"_blank","title":"Contribute","children":"Contribute"}],["$","$L46",null,{"className":"inline-flex shrink-0 cursor-pointer select-none items-center justify-center gap-2 whitespace-nowrap rounded-md text-sm outline-none transition-all ease-out focus-visible:border-ring focus-visible:ring-[3px] focus-visible:ring-ring/50 active:not-aria-[haspopup]:translate-y-px disabled:pointer-events-none disabled:opacity-50 aria-invalid:border-destructive aria-invalid:ring-destructive/20 [&_svg:not([class*='size-'])]:size-4 [&_svg]:pointer-events-none [&_svg]:shrink-0 bg-primary text-primary-foreground shadow-xs hover:bg-[color-mix(in_oklch,var(--primary)_99%,var(--background))] hover:shadow-md h-9 px-4 py-2 has-[>svg]:px-3","href":"/","title":"Home","children":"Home"}]]}]]}]}]]}] 36:o18f,34:[["$","meta","0",{"charSet":"utf-8"}],["$","meta","1",{"name":"viewport","content":"width=device-width, initial-scale=1, viewport-fit=cover, interactive-widget=resizes-visual"}],["$","meta","2",{"name":"theme-color","content":"rgb(255, 255, 255)","media":"(prefers-color-scheme: light)"}],["$","meta","3",{"name":"theme-color","content":"rgb(6, 13, 24)","media":"(prefers-color-scheme: dark)"}]] 36:o67,23:T6,locale2a:T6,locale23:T7,subject2a:T7,subject23:T5,topic2a:T5,topic23:T6,lesson2c:300 2a:T6,lesson36:o8ee,47:I[746880,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"ContentViewTracker"] 36:o18a,30:["$","$L47",null,{"contentId":"asset:en:material:lesson:mathematics:material-section:mathematics:complex-number:multiplication-complex-numbers","context":{"mode":"placement","nodeKey":"class-11-mathematics-complex-number","programKey":"merdeka"},"locale":"en","publicPath":"subjects/mathematics/complex-number/multiplication-complex-numbers","section":"material","children":"$L48"}] 32:null 36:o1077,36:[["$","title","0",{"children":"Multiplication of Complex Numbers"}],["$","meta","1",{"name":"description","content":"Multiply complex numbers using distributive property and formula (x₁x₂-y₁y₂)+i(x₁y₂+x₂y₁). Learn binomial expansion with i²=-1 examples."}],["$","meta","2",{"name":"application-name","content":"Nakafa"}],["$","meta","3",{"name":"author","content":"Nabil Akbarazzima Fatih"}],["$","link","4",{"rel":"manifest","href":"https://nakafa.com/manifest.webmanifest","crossOrigin":"$undefined"}],["$","meta","5",{"name":"generator","content":"Next.js"}],["$","meta","6",{"name":"keywords","content":"free lessons,math lessons,physics lessons,chemistry lessons,biology lessons,computer science lessons,AI lessons,data science lessons,practice questions,worked solutions,exam prep,online try out,K-12 materials,university materials,open education,Nakafa"}],["$","meta","7",{"name":"referrer","content":"origin-when-cross-origin"}],["$","meta","8",{"name":"creator","content":"Nabil Akbarazzima Fatih"}],["$","meta","9",{"name":"publisher","content":"PT. Nakafa Tekno Kreatif"}],["$","meta","10",{"name":"robots","content":"index, follow"}],["$","meta","11",{"name":"googlebot","content":"index, follow, max-video-preview:-1, max-image-preview:large, max-snippet:-1"}],["$","meta","12",{"name":"category","content":"education"}],["$","meta","13",{"name":"classification","content":"Education"}],["$","link","14",{"rel":"canonical","href":"https://nakafa.com/en/subjects/mathematics/complex-number/multiplication-complex-numbers"}],["$","link","15",{"rel":"alternate","hrefLang":"en","href":"https://nakafa.com/en/subjects/mathematics/complex-number/multiplication-complex-numbers"}],["$","link","16",{"rel":"alternate","hrefLang":"id","href":"https://nakafa.com/id/materi/matematika/bilangan-kompleks/perkalian-bilangan-kompleks"}],["$","link","17",{"rel":"alternate","hrefLang":"x-default","href":"https://nakafa.com/en/subjects/mathematics/complex-number/multiplication-complex-numbers"}],["$","link","18",{"rel":"alternate","type":"text/markdown","href":"https://nakafa.com/en/subjects/mathematics/complex-number/multiplication-complex-numbers.md"}],["$","meta","19",{"name":"mobile-web-app-capable","content":"yes"}],["$","meta","20",{"name":"apple-mobile-web-app-title","content":"Nakafa: Free Lessons from K-12 to University"}],["$","meta","21",{"name":"apple-mobile-web-app-status-bar-style","content":"default"}],["$","meta","22",{"property":"og:title","content":"Multiplication of Complex Numbers"}],["$","meta","23",{"property":"og:description","content":"Multiply complex numbers using distributive property and formula (x₁x₂-y₁y₂)+i(x₁y₂+x₂y₁). Learn binomial expansion with i²=-1 examples."}],["$","meta","24",{"property":"og:url","content":"https://nakafa.com/en/subjects/mathematics/complex-number/multiplication-complex-numbers"}],["$","meta","25",{"property":"og:site_name","content":"Nakafa"}],["$","meta","26",{"property":"og:locale","content":"en"}],["$","meta","27",{"property":"og:image","content":"https://nakafa.com/en/og/subjects/mathematics/complex-number/multiplication-complex-numbers/image.png"}],["$","meta","28",{"property":"og:image:width","content":"1200"}],["$","meta","29",{"property":"og:image:height","content":"630"}],["$","meta","30",{"property":"og:image:alt","content":"Multiplication of Complex Numbers"}],["$","meta","31",{"property":"og:type","content":"article"}],["$","meta","32",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","33",{"name":"twitter:site","content":"@nabilfatih_"}],["$","meta","34",{"name":"twitter:creator","content":"@nabilfatih_"}],["$","meta","35",{"name":"twitter:title","content":"Multiplication of Complex Numbers"}],["$","meta","36",{"name":"twitter:description","content":"Multiply complex numbers using distributive property and formula (x₁x₂-y₁y₂)+i(x₁y₂+x₂y₁). Learn binomial expansion with i²=-1 examples."}],["$","meta","37",{"name":"twitter:image","content":"https://nakafa.com/en/og/subjects/mathematics/complex-number/multiplication-complex-numbers/image.png"}],"$L49","$L4a","$L4b","$L4c","$L4d","$L4e","$L4f","$L50","$L51","$L52","$L53","$L54","$L55"] 36:o874,56:I[243099,["/_next/static/immutable/chunks/2_93dzz8su_du.js"],"IconMark"] 49:["$","meta","38",{"name":"twitter:image:alt","content":"Multiplication of Complex Numbers"}] 4a:["$","meta","39",{"name":"twitter:image:width","content":"1200"}] 4b:["$","meta","40",{"name":"twitter:image:height","content":"630"}] 4c:["$","link","41",{"rel":"shortcut icon","href":"/favicon.ico"}] 4d:["$","link","42",{"rel":"shortcut icon","href":"https://nakafa.com/favicon.ico"}] 4e:["$","link","43",{"rel":"icon","href":"/favicon.ico","sizes":"16x16","type":"image/x-icon"}] 4f:["$","link","44",{"rel":"icon","href":"/logo.svg","type":"image/svg+xml"}] 50:["$","link","45",{"rel":"icon","href":"https://nakafa.com/favicon.ico"}] 51:["$","link","46",{"rel":"apple-touch-icon","href":"/logo.svg"}] 52:["$","link","47",{"rel":"apple-touch-icon","href":"https://nakafa.com/logo.svg"}] 53:["$","link","48",{"rel":"manifest","href":"/manifest.webmanifest"}] 54:["$","link","49",{"rel":"apple-touch-icon","href":"/logo.svg"}] 55:["$","$L56","50",{}] 57:T46a,{"@context":"https://schema.org","@type":"Article","name":"Multiplication of Complex Numbers","headline":"Multiplication of Complex Numbers","url":"https://nakafa.com/en/subjects/mathematics/complex-number/multiplication-complex-numbers","mainEntityOfPage":{"@type":"WebPage","@id":"https://nakafa.com/en/subjects/mathematics/complex-number/multiplication-complex-numbers"},"datePublished":"2025-05-01T00:00:00.000Z","dateModified":"2025-05-01T00:00:00.000Z","author":[{"@type":"Person","name":"Nabil Akbarazzima Fatih","url":"https://nakafa.com/en/contributor"}],"image":["https://nakafa.com/en/og/subjects/mathematics/complex-number/multiplication-complex-numbers/image.png"],"description":"Multiply complex numbers using distributive property and formula (x₁x₂-y₁y₂)+i(x₁y₂+x₂y₁). Learn binomial expansion with i²=-1 examples.","publisher":{"@type":"Organization","name":"Nakafa","legalName":"PT. Nakafa Tekno Kreatif","url":"https://nakafa.com","logo":"https://nakafa.com/logo.svg","sameAs":["https://twitter.com/nabilfatih_","https://www.linkedin.com/company/nakafa","https://www.instagram.com/nakafa.ai/"]}}36:oae4,48:[["$","script",null,{"dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://nakafa.com/en\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Multiplication of Complex Numbers\",\"item\":\"https://nakafa.com/en/subjects/mathematics/complex-number/multiplication-complex-numbers\"}]}"},"id":"json-ld-8zkzz7","type":"application/ld+json"}],["$","script",null,{"dangerouslySetInnerHTML":{"__html":"$57"},"id":"json-ld-ire87h","type":"application/ld+json"}],["$","script",null,{"dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"LearningResource\",\"name\":\"Multiplication of Complex Numbers\",\"description\":\"Multiply complex numbers using distributive property and formula (x₁x₂-y₁y₂)+i(x₁y₂+x₂y₁). Learn binomial expansion with i²=-1 examples.\",\"educationalLevel\":\"Complex Number\",\"datePublished\":\"2025-05-01T00:00:00.000Z\",\"author\":[{\"@type\":\"Person\",\"name\":\"Nabil Akbarazzima Fatih\",\"url\":\"https://nakafa.com/en/contributor\"}],\"publisher\":{\"@type\":\"Organization\",\"name\":\"Nakafa\",\"legalName\":\"PT. Nakafa Tekno Kreatif\",\"url\":\"https://nakafa.com\",\"logo\":\"https://nakafa.com/logo.svg\",\"sameAs\":[\"https://twitter.com/nabilfatih_\",\"https://www.linkedin.com/company/nakafa\",\"https://www.instagram.com/nakafa.ai/\"]},\"maintainer\":{\"@type\":\"Organization\",\"name\":\"Nakafa\",\"legalName\":\"PT. Nakafa Tekno Kreatif\",\"url\":\"https://nakafa.com\",\"logo\":\"https://nakafa.com/logo.svg\",\"sameAs\":[\"https://twitter.com/nabilfatih_\",\"https://www.linkedin.com/company/nakafa\",\"https://www.instagram.com/nakafa.ai/\"]}}"},"id":"json-ld-fhhiz2","type":"application/ld+json"}],["$","div",null,{"className":"min-w-0 flex-1","children":[["$","header",null,{"className":"relative py-20","children":["$","div",null,{"className":"z-10 mx-auto max-w-3xl space-y-6 px-6","children":[["$","div",null,{"className":"flex flex-col gap-3","children":[["$","$L46",null,{"aria-label":"Complex Numbers","className":"w-fit font-medium text-primary text-sm underline-offset-4 hover:underline","href":"/en/curriculum/merdeka/class-11/mathematics#complex-numbers","title":"Complex Numbers","children":"Complex Numbers"}],["$","div",null,{"className":"flex items-start gap-2","children":[["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"hidden size-7 shrink-0 translate-y-1 sm:block","strokeWidth":2,"stroke":"currentColor","children":["$L58","$L59","$L5a"]}],"$L5b"]}]]}],false,"$L5c"]}]}],"$L5d","$L5e","$L5f","$L60"]}],"$L61"] 36:o8e6,62:I[83208,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"OpenContent"] 36:o8ec,7d:I[732920,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"DeferredComments"] 36:o8ef,7e:I[469866,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"DeferredAiSheetOpen"] 36:o8eb,7f:I[180806,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"SidebarProvider"] 36:o8e9,80:I[53973,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"SidebarTrigger"] 36:o8e2,81:I[53973,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"Sidebar"] 36:o8e9,82:I[165141,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"SidebarHeader"] 36:o8e7,83:I[866847,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"SidebarMenu"] 36:o8eb,84:I[866847,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"SidebarMenuItem"] 36:o8ed,85:I[866847,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"SidebarMenuButton"] 36:o8f2,86:I[866847,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"SidebarMenuDescription"] 36:o8ea,87:I[165141,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"SidebarContent"] 36:o8e7,88:I[506072,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"SidebarTree"] 36:o8e9,89:I[165141,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"SidebarFooter"] 36:o8ea,8a:I[399726,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"CommentsButton"] 36:o8e7,8d:I[100455,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"ShareButton"] 36:o33e,58:["$","path","0",{"d":"M3 9.3C3 7.5 5.06126 5.7 7.68468 5.7L16.9574 5.7C19.2 5.7 21 4.35 21 3","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}] 59:["$","path","1",{"d":"M16.502 6L15.6072 18.3139C15.5177 19.7653 16.5097 20.9999 17.7654 20.9999C18.6967 20.9999 19.5236 20.3093 19.8181 19.2855L20.1016 18.2999","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}] 5a:["$","path","2",{"d":"M10 6C9.86667 9.0625 9.6 14.75 9.2 16.5C8.8 18.25 8 20 6 20","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}] 5b:["$","h1",null,{"className":"font-medium text-3xl leading-tight tracking-tight","children":"Multiplication of Complex Numbers"}] 63:T12d5,36:o12d5, export const metadata = { title: "Multiplication of Complex Numbers", description: "Multiply complex numbers using distributive property and formula (x₁x₂-y₁y₂)+i(x₁y₂+x₂y₁). Learn binomial expansion with i²=-1 examples.", authors: [{ name: "Nabil Akbarazzima Fatih" }], date: "2025-05-01", subject: "Complex Number", }; ## Multiplying Two Complex Numbers Multiplying two complex numbers is similar to multiplying two binomial algebraic expressions. We can use the distributive property of multiplication over addition. Let's see how to multiply by . Remember that , so we can substitute: Now, let's group the real and imaginary parts: So, the general formula for complex number multiplication is: ## Calculation Example Let and . Find . **Solution:** Using the distributive property: Or using the general formula with : The result is the same! Visualization of ,{" "} , and their product{" "} . } cameraPosition={[0, 0, 15]} showZAxis={false} data={[ { points: [ { x: 0, y: 0, z: 0 }, { x: 2, y: 1, z: 0 }, ], color: "#0284c7", labels: [{ text: "z₁ = 2+i", at: 1, offset: [0.5, 0.5, 0] }], cone: { position: "end" }, }, { points: [ { x: 0, y: 0, z: 0 }, { x: 1, y: -2, z: 0 }, ], color: "#059669", labels: [{ text: "z₂ = 1-2i", at: 1, offset: [0.5, -0.5, 0] }], cone: { position: "end" }, }, { points: [ { x: 0, y: 0, z: 0 }, { x: 4, y: -3, z: 0 }, ], color: "#e11d48", labels: [{ text: "z₁ × z₂ = 4-3i", at: 1, offset: [0.5, -0.5, 0] }], cone: { position: "end" }, }, ]} /> ## Exercise Let and . Find . ### Answer Key Using the distributive property: Using the general formula with : 36:o13f,5c:["$","$L62",null,{"content":"$63","slug":"/en/subjects/mathematics/complex-number/multiplication-complex-numbers","sourceUrl":"https://github.com/nakafaai/aksara/blob/a48d644c809419c93dc247239eabba9ced519051/packages/corpus/material/lesson/mathematics/complex-number/multiplication-complex-numbers/en.mdx"}] 64:Tab0,36:oab0,

z_1 = x_1 + iy_1

36:o869,5d:["$","article",null,{"className":"mx-auto max-w-3xl px-6","children":[false,[["$","h2",null,{"className":"mt-10 mb-6 flex scroll-mt-44 items-center font-medium tracking-tight first:mt-0 last:mb-0 text-2xl","id":"multiplying-two-complex-numbers","children":["$","a",null,{"aria-label":"Link to Multiplying Two Complex Numbers","className":"group/heading inline-flex items-center gap-4","href":"#multiplying-two-complex-numbers","title":"Multiplying Two Complex Numbers","children":[["$","span",null,{"className":"text-pretty","children":"Multiplying Two Complex Numbers"}],["$","div",null,{"className":"rounded-sm border p-2 opacity-0 transition-opacity ease-out group-hover/heading:opacity-100","children":["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0 text-muted-foreground","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M13.5 17H17C19.7614 17 22 14.7614 22 12C22 9.23858 19.7614 7 17 7H13.5M10.5 17H7C4.23858 17 2 14.7614 2 12C2 9.23858 4.23858 7 7 7H10.5","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}],["$","path","1",{"d":"M9 12H15","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}]]}]}]]}]}],"\n",["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"Multiplying two complex numbers is similar to multiplying two binomial algebraic expressions. We can use the distributive property of multiplication over addition."}],"\n",["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Let's see how to multiply ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$64"}}]}]," by ","$L65","."]}],"\n","$L66","\n","$L67","\n","$L68","\n","$L69","\n","$L6a","\n","$L6b","\n","$L6c","\n","$L6d","\n","$L6e","\n","$L6f","\n","$L70","\n","$L71","\n","$L72","\n","$L73","\n","$L74","\n","$L75","\n","$L76","\n","$L77","\n","$L78","\n","$L79","\n","$L7a","\n","$L7b","\n","$L7c"]]}] 36:o1be,5f:["$","footer",null,{"className":"relative py-20","children":["$","div",null,{"className":"z-10 mx-auto max-w-3xl px-6","children":["$","$L7d",null,{"slug":"material/lesson/mathematics/complex-number/multiplication-complex-numbers"}]}]}] 60:["$","$L7e",null,{"audio":{"contentType":"material","locale":"en","slug":"material/lesson/mathematics/complex-number/multiplication-complex-numbers"},"contextTitle":"Multiplication of Complex Numbers"}] 36:o7b0,61:["$","aside",null,{"children":["$","$L7f",null,{"cookieName":"sidebar_state:right","keyboardShortcut":"x","sidebarDesktop":1280,"children":[["$","$L80",null,{"className":"fixed top-20 right-6 size-9 bg-background/80 backdrop-blur-xs xl:hidden","icon":[["path",{"d":"M4 5L16 5","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":"1.5","key":"0"}],["path",{"d":"M4 12L20 12","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":"1.5","key":"1"}],["path",{"d":"M4 19L12 19","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":"1.5","key":"2"}]],"size":"icon","variant":"outline"}],["$","$L81",null,{"containerClassName":"lg:hidden xl:block","side":"right","children":[["$","$L82",null,{"children":["$","$L83",null,{"children":["$","$L84",null,{"children":["$","$L85",null,{"render":["$","$L46",null,{"href":"/en/subjects/mathematics/complex-number/multiplication-complex-numbers","title":"Multiplication of Complex Numbers"}],"size":"lg","children":["$","div",null,{"className":"grid flex-1 text-left text-sm leading-tight","children":[["$","span",null,{"className":"truncate font-medium","children":"Multiplication of Complex Numbers"}],["$","$L86",null,{"children":"Multiply complex numbers using distributive property and formula (x₁x₂-y₁y₂)+i(x₁y₂+x₂y₁). Learn binomial expansion with i²=-1 examples."}]]}]}]}]}]}],["$","$L87",null,{"children":["$","$L88",null,{"data":[{"label":"Multiplying Two Complex Numbers","href":"#multiplying-two-complex-numbers","children":[]},{"label":"Calculation Example","href":"#calculation-example","children":[]},{"label":"Exercise","href":"#exercise","children":[{"label":"Answer Key","href":"#answer-key","children":[]}]}],"title":"On this page"}]}],["$","$L89",null,{"className":"border-t","children":["$","$L83",null,{"children":[["$","$L8a",null,{}],false,"$L8b","$L8c",["$","$L8d",null,{}]]}]}]]}]]}]}] 36:o8e6,8f:I[416523,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"ScrollArea"] 36:o8e2,c7:I[776218,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"Button"] 36:o8,8e:Tab0,36:oab0,

z_2 = x_2 + iy_2

36:oa0,65:["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$8e"}}]}] 90:T1504,36:o1504,

z_1 \times z_2 = (x_1 + iy_1)(x_2 + iy_2)

36:o83e,66:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$90"}}]}],"$L91"]}]}],"$L92","$L93"]}] 94:T454,

i^2 = -1

67:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Remember that ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$94"}}]}],", so we can substitute:"]}] 95:T19f0,36:o19f0,

= (x_1x_2 + ix_1y_2) + (ix_2y_1 + (-1)y_1y_2)

36:o353,68:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-compact","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$95"}}]}],"$L96"]}]}],"$L97"]}] 69:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"Now, let's group the real and imaginary parts:"}] 98:T1933,36:o1933,

= (x_1x_2 - y_1y_2) + (ix_1y_2 + ix_2y_1)

36:o362,6a:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-compact","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$98"}}]}],"$L99"]}]}],"$L9a"]}] 6b:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"So, the general formula for complex number multiplication is:"}] 9b:T1f2b,36:o1f2b,

z_1 \times z_2 = (x_1x_2 - y_1y_2) + i(x_1y_2 + x_2y_1)

36:o5f9,6c:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$9b"}}]}],"$L9c"]}]}] 6d:["$","h2",null,{"className":"mt-10 mb-6 flex scroll-mt-44 items-center font-medium tracking-tight first:mt-0 last:mb-0 text-2xl","id":"calculation-example","children":["$","a",null,{"aria-label":"Link to Calculation Example","className":"group/heading inline-flex items-center gap-4","href":"#calculation-example","title":"Calculation Example","children":[["$","span",null,{"className":"text-pretty","children":"Calculation Example"}],["$","div",null,{"className":"rounded-sm border p-2 opacity-0 transition-opacity ease-out group-hover/heading:opacity-100","children":["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0 text-muted-foreground","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M13.5 17H17C19.7614 17 22 14.7614 22 12C22 9.23858 19.7614 7 17 7H13.5M10.5 17H7C4.23858 17 2 14.7614 2 12C2 9.23858 4.23858 7 7 7H10.5","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}],["$","path","1",{"d":"M9 12H15","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}]]}]}]]}]}] 9d:T613,36:o613,

z_1 = 2+i

36:o8,9e:T63d,36:o63d,

z_2 = 1-2i

36:o310,6e:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Let ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$9d"}}]}]," and ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$9e"}}]}],". Find ","$L9f","."]}] 6f:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["$","strong",null,{"className":"font-medium","children":"Solution:"}]}] 70:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"Using the distributive property:"}] a0:Tc20,36:oc20,

z_1 \times z_2 = (2+i)(1-2i)

36:o2d6,71:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-spacious","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$a0"}}]}],"$La1"]}]}],"$La2","$La3","$La4","$La5","$La6","$La7"]}] a8:T10f2,36:o10f2,

x_1 = 2, y_1 = 1, x_2 = 1, y_2 = -2

36:o138,72:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Or using the general formula with ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$a8"}}]}],":"]}] a9:T1f2b,36:o1f2b,

z_1 \times z_2 = (x_1x_2 - y_1y_2) + i(x_1y_2 + x_2y_1)

36:o351,73:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-spacious","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$a9"}}]}],"$Laa"]}]}],"$Lab","$Lac","$Lad","$Lae"]}] 74:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"The result is the same!"}] af:T613,36:o613,

z_1 = 2+i

36:o8,b0:T63d,36:o63d,

z_2 = 1-2i

36:o83e,75:["$","div",null,{"className":"flex flex-col gap-6 rounded-xl border bg-card py-6 text-card-foreground shadow-sm content-auto-card","data-slot":"card","children":[["$","div",null,{"className":"@container/card-header grid auto-rows-min grid-rows-[auto_auto] items-start gap-2 px-6 has-data-[slot=card-action]:grid-cols-[1fr_auto] [.border-b]:pb-6","data-slot":"card-header","children":[["$","div",null,{"className":"font-medium leading-tight","data-slot":"card-title","children":"Visualization of Complex Number Multiplication"}],["$","div",null,{"className":"text-muted-foreground text-sm","data-slot":"card-description","children":["Visualization of ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$af"}}]}],","," ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$b0"}}]}],", and their product"," ","$Lb1","."]}]]}],"$Lb2"]}] 76:["$","h2",null,{"className":"mt-10 mb-6 flex scroll-mt-44 items-center font-medium tracking-tight first:mt-0 last:mb-0 text-2xl","id":"exercise","children":["$","a",null,{"aria-label":"Link to Exercise","className":"group/heading inline-flex items-center gap-4","href":"#exercise","title":"Exercise","children":[["$","span",null,{"className":"text-pretty","children":"Exercise"}],["$","div",null,{"className":"rounded-sm border p-2 opacity-0 transition-opacity ease-out group-hover/heading:opacity-100","children":["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0 text-muted-foreground","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M13.5 17H17C19.7614 17 22 14.7614 22 12C22 9.23858 19.7614 7 17 7H13.5M10.5 17H7C4.23858 17 2 14.7614 2 12C2 9.23858 4.23858 7 7 7H10.5","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}],["$","path","1",{"d":"M9 12H15","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}]]}]}]]}]}] b3:T613,36:o613,

z_1 = 1+i

36:o8,b4:T9ed,36:o9ed,

z_2 = \frac{1}{2} - 2i

36:o6a4,77:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Let ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$b3"}}]}]," and ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$b4"}}]}],". Find ","$Lb5","."]}] 78:["$","h3",null,{"className":"mt-10 mb-6 flex scroll-mt-44 items-center font-medium tracking-tight first:mt-0 last:mb-0 text-xl","id":"answer-key","children":["$","a",null,{"aria-label":"Link to Answer Key","className":"group/heading inline-flex items-center gap-4","href":"#answer-key","title":"Answer Key","children":[["$","span",null,{"className":"text-pretty","children":"Answer Key"}],["$","div",null,{"className":"rounded-sm border p-2 opacity-0 transition-opacity ease-out group-hover/heading:opacity-100","children":["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0 text-muted-foreground","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M13.5 17H17C19.7614 17 22 14.7614 22 12C22 9.23858 19.7614 7 17 7H13.5M10.5 17H7C4.23858 17 2 14.7614 2 12C2 9.23858 4.23858 7 7 7H10.5","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}],["$","path","1",{"d":"M9 12H15","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}]]}]}]]}]}] 79:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"Using the distributive property:"}] b6:Tf51,36:of51,

z_1 \times z_2 = (1+i)(\frac{1}{2} - 2i)

36:o2dd,7a:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-spacious","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$b6"}}]}],"$Lb7"]}]}],"$Lb8","$Lb9","$Lba","$Lbb","$Lbc","$Lbd","$Lbe"]}] bf:T14a0,36:o14a0,

x_1 = 1, y_1 = 1, x_2 = \frac{1}{2}, y_2 = -2

36:o135,7b:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Using the general formula with ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$bf"}}]}],":"]}] c0:T1f2b,36:o1f2b,

z_1 \times z_2 = (x_1x_2 - y_1y_2) + i(x_1y_2 + x_2y_1)

36:o2c6,7c:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-spacious","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$c0"}}]}],"$Lc1"]}]}],"$Lc2","$Lc3","$Lc4","$Lc5","$Lc6"]}] 36:ob0e,5e:["$","nav",null,{"aria-label":"Pagination navigation","className":"mt-10 pt-10","children":["$","div",null,{"className":"mx-auto grid max-w-3xl gap-6 px-6 sm:grid-cols-2","children":[["$","$Lc7",null,{"className":"group flex h-auto flex-col whitespace-normal py-3 shadow-xs items-start","nativeButton":false,"render":["$","$L46",null,{"href":"/en/subjects/mathematics/complex-number/modulus-argument-complex-numbers?ctx=merdeka~class-11-mathematics-complex-number","title":"Modulus and Argument of Complex Numbers","children":[["$","div",null,{"className":"flex items-center gap-2 font-normal text-muted-foreground text-sm transition-colors group-hover:text-accent-foreground","children":[["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M5.5 12.002H19","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M10.9999 18.002C10.9999 18.002 4.99998 13.583 4.99997 12.0019C4.99996 10.4208 11 6.00195 11 6.00195","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}]]}],"Previous",false]}],["$","p",null,{"className":"w-full text-foreground transition-colors group-hover:text-accent-foreground","children":"Modulus and Argument of Complex Numbers"}]]}],"variant":"outline"}],["$","$Lc7",null,{"className":"group flex h-auto flex-col whitespace-normal py-3 shadow-xs items-end","nativeButton":false,"render":["$","$L46",null,{"href":"/en/subjects/mathematics/complex-number/principal-argument-complex-numbers?ctx=merdeka~class-11-mathematics-complex-number","title":"Principal Argument of Complex Numbers","children":[["$","div",null,{"className":"flex items-center gap-2 font-normal text-muted-foreground text-sm transition-colors group-hover:text-accent-foreground","children":[false,"Next",["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M18.5 12L4.99997 12","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M13 18C13 18 19 13.5811 19 12C19 10.4188 13 6 13 6","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}]]}]]}],["$","p",null,{"className":"w-full text-foreground transition-colors group-hover:text-accent-foreground text-right","children":"Principal Argument of Complex Numbers"}]]}],"variant":"outline"}]]}]}] 36:oc90,8b:["$","$L84",null,{"children":["$","$L85",null,{"render":["$","a",null,{"aria-label":"Report","href":"https://github.com/nakafaai/nakafa.com/issues/new/choose","rel":"noopener noreferrer","target":"_blank","title":"Report","children":[["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M3.01206 6.59744C2.89214 7.65674 3.6584 10.1951 5.87693 10.255","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M18.2891 10.195C19.3684 10.255 20.9873 8.99582 20.9873 6.59741","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","2",{"d":"M20.0876 20.9879C20.1476 19.6088 19.2482 17.4742 17.5093 17.4142","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","3",{"d":"M3.90138 20.9881C3.84009 19.5998 4.7594 17.4509 6.53675 17.3905","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","4",{"d":"M3.01227 13.7926H5.21757","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","5",{"d":"M21 13.7926L18.8282 13.7926","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","6",{"d":"M11.9932 13.7926V10.8546M16.4902 2.99982L14.6914 4.79862M7.49615 2.99982L9.29496 4.79862","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","7",{"d":"M6.95612 8.61209C8.57504 9.77532 12.5924 11.4542 16.9695 8.68404","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","8",{"d":"M16.826 7.6767C13.2523 2.7 8.69536 5.09841 7.07644 7.8206C6.02093 9.59542 4.37823 13.8886 7.49616 18.5655C10.8539 22.6667 14.8113 20.808 16.4302 18.6494C17.9892 16.7906 19.5242 11.9938 16.826 7.6767Z","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}]]}],["$","span",null,{"className":"truncate","children":"Report"}],["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"ml-auto size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M11.0991 3.00012C7.45013 3.00669 5.53932 3.09629 4.31817 4.31764C3.00034 5.63568 3.00034 7.75704 3.00034 11.9997C3.00034 16.2424 3.00034 18.3638 4.31817 19.6818C5.63599 20.9999 7.75701 20.9999 11.9991 20.9999C16.241 20.9999 18.3621 20.9999 19.6799 19.6818C20.901 18.4605 20.9906 16.5493 20.9972 12.8998","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M20.556 3.49612L11.0487 13.0586M20.556 3.49612C20.062 3.00151 16.7343 3.04761 16.0308 3.05762M20.556 3.49612C21.05 3.99074 21.0039 7.32273 20.9939 8.02714","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}]]}]]}],"tooltip":"Report"}]}] 36:obc2,8c:["$","$L84",null,{"children":["$","$L85",null,{"render":["$","a",null,{"aria-label":"Source code","href":"https://github.com/nakafaai/aksara/blob/a48d644c809419c93dc247239eabba9ced519051/packages/corpus/material/lesson/mathematics/complex-number/multiplication-complex-numbers/en.mdx","rel":"noopener noreferrer","target":"_blank","title":"Source code","children":[["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M10 20.5675C6.57143 21.7248 3.71429 20.5675 2 17","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M10 22V18.7579C10 18.1596 10.1839 17.6396 10.4804 17.1699C10.6838 16.8476 10.5445 16.3904 10.1771 16.2894C7.13394 15.4528 5 14.1077 5 9.64606C5 8.48611 5.38005 7.39556 6.04811 6.4464C6.21437 6.21018 6.29749 6.09208 6.31748 5.9851C6.33746 5.87813 6.30272 5.73852 6.23322 5.45932C5.95038 4.32292 5.96871 3.11619 6.39322 2.02823C6.39322 2.02823 7.27042 1.74242 9.26698 2.98969C9.72282 3.27447 9.95075 3.41686 10.1515 3.44871C10.3522 3.48056 10.6206 3.41384 11.1573 3.28041C11.8913 3.09795 12.6476 3 13.5 3C14.3524 3 15.1087 3.09795 15.8427 3.28041C16.3794 3.41384 16.6478 3.48056 16.8485 3.44871C17.0493 3.41686 17.2772 3.27447 17.733 2.98969C19.7296 1.74242 20.6068 2.02823 20.6068 2.02823C21.0313 3.11619 21.0496 4.32292 20.7668 5.45932C20.6973 5.73852 20.6625 5.87813 20.6825 5.9851C20.7025 6.09207 20.7856 6.21019 20.9519 6.4464C21.6199 7.39556 22 8.48611 22 9.64606C22 14.1077 19.8661 15.4528 16.8229 16.2894C16.4555 16.3904 16.3162 16.8476 16.5196 17.1699C16.8161 17.6396 17 18.1596 17 18.7579V22","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}]]}],["$","span",null,{"className":"truncate","children":"Source code"}],["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"ml-auto size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M11.0991 3.00012C7.45013 3.00669 5.53932 3.09629 4.31817 4.31764C3.00034 5.63568 3.00034 7.75704 3.00034 11.9997C3.00034 16.2424 3.00034 18.3638 4.31817 19.6818C5.63599 20.9999 7.75701 20.9999 11.9991 20.9999C16.241 20.9999 18.3621 20.9999 19.6799 19.6818C20.901 18.4605 20.9906 16.5493 20.9972 12.8998","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M20.556 3.49612L11.0487 13.0586M20.556 3.49612C20.062 3.00151 16.7343 3.04761 16.0308 3.05762M20.556 3.49612C21.05 3.99074 21.0039 7.32273 20.9939 8.02714","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}]]}]]}],"tooltip":"Source code"}]}] 36:o8e5,c8:I[416523,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"ScrollBar"] 36:o8eb,dc:I[72382,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"CoordinateSystem"] 36:o8e8,dd:I[853472,["/_next/static/immutable/chunks/2ozbzbkbjrs5g.js","/_next/static/immutable/chunks/1u94c24vqx26q.js","/_next/static/immutable/chunks/44psnuid4hcf5.js","/_next/static/immutable/chunks/2b2z9fhnbh5e0.js","/_next/static/immutable/chunks/0ni87mxribyly.js","/_next/static/immutable/chunks/0g7ln_b7f132w.js","/_next/static/immutable/chunks/1bapa2m2ksez8.js","/_next/static/immutable/chunks/0ugejllqhnrwj.js","/_next/static/immutable/chunks/1gze7y7ht-33b.js","/_next/static/immutable/chunks/393_w_-eb8uv-.js","/_next/static/immutable/chunks/0chv-zggdaw_f.js","/_next/static/immutable/chunks/287vic71a6h_7.js","/_next/static/immutable/chunks/2tmwfq8jsbwhd.js","/_next/static/immutable/chunks/136a_3pwwx3sd.js","/_next/static/immutable/chunks/1j7t38u2zaqis.js","/_next/static/immutable/chunks/02shfbk-zzfca.js","/_next/static/immutable/chunks/2d0hfm5dv_pzb.js","/_next/static/immutable/chunks/1k-yr9yysem7x.js","/_next/static/immutable/chunks/06f0haa4q81t6.js","/_next/static/immutable/chunks/0kbnvbl7eptep.js","/_next/static/immutable/chunks/3brmn4mcym1z7.js","/_next/static/immutable/chunks/0_ln2_6lkmx32.js","/_next/static/immutable/chunks/2tvds67b366ea.js","/_next/static/immutable/chunks/442lhk44e6ykq.js","/_next/static/immutable/chunks/3b6wkamawtv3r.js","/_next/static/immutable/chunks/2rdc3wpvx-0y9.js","/_next/static/immutable/chunks/3b0fdgj_zftzq.js","/_next/static/immutable/chunks/27ei9vnzeiq85.js","/_next/static/immutable/chunks/014aoh0qn81eo.js","/_next/static/immutable/chunks/1c00lzvzs706d.js","/_next/static/immutable/chunks/3ywgyv40llk3m.js","/_next/static/immutable/chunks/058g38eq00elg.js","/_next/static/immutable/chunks/1rug2kwvfis1u.js","/_next/static/immutable/chunks/21b3i3nowssv-.js","/_next/static/immutable/chunks/2qkbg9ig3vnaf.js","/_next/static/immutable/chunks/2zves0p1ggtcw.js","/_next/static/immutable/chunks/3cpp7c7yc-8su.js","/_next/static/immutable/chunks/1l-5amv9gm5ec.js","/_next/static/immutable/chunks/2yr4tqc4fd3s6.js","/_next/static/immutable/chunks/36ofm1pm6eeme.js","/_next/static/immutable/chunks/05s1116x2xxgz.js","/_next/static/immutable/chunks/34f45g3k3ibf_.js","/_next/static/immutable/chunks/1uw8afofehcs7.js","/_next/static/immutable/chunks/3wms78zzv6zr5.js","/_next/static/immutable/chunks/3s93rqpoi-ptk.js"],"LineEquation"] 36:o3b,91:["$","$Lc8",null,{"orientation":"horizontal"}] c9:T14b5,36:o14b5,

= x_1(x_2 + iy_2) + iy_1(x_2 + iy_2)

36:o181,92:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$c9"}}]}],"$Lca"]}]}] cb:T1ae3,36:o1ae3,

= (x_1x_2 + ix_1y_2) + (ix_2y_1 + i^2y_1y_2)

36:o1b3,93:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$cb"}}]}],"$Lcc"]}]}] 96:["$","$Lc8",null,{"orientation":"horizontal"}] cd:T1868,36:o1868,

= x_1x_2 + ix_1y_2 + ix_2y_1 - y_1y_2

36:o1b3,97:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$cd"}}]}],"$Lce"]}]}] 99:["$","$Lc8",null,{"orientation":"horizontal"}] cf:T1902,36:o1902,

= (x_1x_2 - y_1y_2) + i(x_1y_2 + x_2y_1)

36:o1b2,9a:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$cf"}}]}],"$Ld0"]}]}] 9c:["$","$Lc8",null,{"orientation":"horizontal"}] d1:T73d,36:o73d,

z_1 \times z_2

36:od1,9f:["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$d1"}}]}] a1:["$","$Lc8",null,{"orientation":"horizontal"}] d2:T776,36:o776,

= 2(1-2i) + i(1-2i)

36:o1a8,a2:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$d2"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] d3:T8b1,36:o8b1,

= (2 - 4i) + (i - 2i^2)

36:o1a8,a3:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$d3"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] d4:Tb96,36:ob96,

= (2 - 4i) + (i - 2(-1)) \quad \text{(since } i^2 = -1)

36:o180,a4:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$d4"}}]}],"$Ld5"]}]}] d6:T6f9,36:o6f9,

= (2 - 4i) + (i + 2)

36:o1a8,a5:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$d6"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] d7:T71d,36:o71d,

= (2+2) + (-4i + i)

36:o1a0,a6:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$d7"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] 36:o58e,a7:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"

= 4 - 3i

"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] 36:o3a,aa:["$","$Lc8",null,{"orientation":"horizontal"}] d8:Taba,36:oaba,

= (2)(1) - (1)(-2) + i((2)(-2) + (1)(1))

36:o1a8,ab:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$d8"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] d9:T797,36:o797,

= (2 - (-2)) + i(-4 + 1)

36:o1a8,ac:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$d9"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] da:T5ee,36:o5ee,

= (2+2) + i(-3)

36:o1a0,ad:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$da"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] 36:o58e,ae:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"

= 4 - 3i

"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] 36:o8,db:T9ad,36:o9ad,

z_1 \times z_2 = 4-3i

36:o385,b1:["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$db"}}]}] b2:["$","div",null,{"className":"px-6","data-slot":"card-content","children":["$","$Ldc",null,{"cameraPosition":[0,0,15],"showZAxis":false,"children":[["$","$Ldd","line-0,0,0;2,1,0",{"points":[{"x":0,"y":0,"z":0},{"x":2,"y":1,"z":0}],"color":"#0284c7","labels":[{"text":"z₁ = 2+i","at":1,"offset":[0.5,0.5,0]}],"cone":{"position":"end"}}],["$","$Ldd","line-0,0,0;1,-2,0",{"points":[{"x":0,"y":0,"z":0},{"x":1,"y":-2,"z":0}],"color":"#059669","labels":[{"text":"z₂ = 1-2i","at":1,"offset":[0.5,-0.5,0]}],"cone":{"position":"end"}}],["$","$Ldd","line-0,0,0;4,-3,0",{"points":[{"x":0,"y":0,"z":0},{"x":4,"y":-3,"z":0}],"color":"#e11d48","labels":[{"text":"z₁ × z₂ = 4-3i","at":1,"offset":[0.5,-0.5,0]}],"cone":{"position":"end"}}]]}]}] de:T73d,36:o73d,

z_1 \times z_2

36:od1,b5:["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$de"}}]}] b7:["$","$Lc8",null,{"orientation":"horizontal"}] df:Tdd8,36:odd8,

= 1(\frac{1}{2} - 2i) + i(\frac{1}{2} - 2i)

36:o180,b8:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$df"}}]}],"$Le0"]}]}] e1:Tf35,36:of35,

= (\frac{1}{2} - 2i) + (\frac{1}{2}i - 2i^2)

36:o180,b9:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$e1"}}]}],"$Le2"]}]}] e3:Te26,36:oe26,

= (\frac{1}{2} - 2i) + (\frac{1}{2}i - 2(-1))

36:o180,ba:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$e3"}}]}],"$Le4"]}]}] e5:Td7d,36:od7d,

= (\frac{1}{2} - 2i) + (\frac{1}{2}i + 2)

36:o180,bb:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$e5"}}]}],"$Le6"]}]}] e7:Tda3,36:oda3,

= (\frac{1}{2} + 2) + (-2i + \frac{1}{2}i)

36:o181,bc:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$e7"}}]}],"$Le8"]}]}] e9:T1401,36:o1401,

= (\frac{1}{2} + \frac{4}{2}) + (-\frac{4}{2}i + \frac{1}{2}i)

36:o180,bd:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$e9"}}]}],"$Lea"]}]}] eb:Ta22,36:oa22,

= \frac{5}{2} - \frac{3}{2}i

36:o1db,be:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$eb"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] c1:["$","$Lc8",null,{"orientation":"horizontal"}] ec:T1152,36:o1152,

= ((1)(\frac{1}{2}) - (1)(-2)) + i((1)(-2) + (\frac{1}{2})(1))

36:o180,c2:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$ec"}}]}],"$Led"]}]}] ee:Tdf5,36:odf5,

= (\frac{1}{2} - (-2)) + i(-2 + \frac{1}{2})

36:o181,c3:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$ee"}}]}],"$Lef"]}]}] f0:T10a1,36:o10a1,

= (\frac{1}{2} + 2) + i(-\frac{4}{2} + \frac{1}{2})

36:o180,c4:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$f0"}}]}],"$Lf1"]}]}] f2:Tf7d,36:of7d,

= (\frac{1}{2} + \frac{4}{2}) + i(-\frac{3}{2})

36:o180,c5:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$f2"}}]}],"$Lf3"]}]}] f4:Ta22,36:oa22,

= \frac{5}{2} - \frac{3}{2}i

36:o1a0,c6:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L8f",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$f4"}}]}],["$","$Lc8",null,{"orientation":"horizontal"}]]}]}] 36:o2ee,ca:["$","$Lc8",null,{"orientation":"horizontal"}] cc:["$","$Lc8",null,{"orientation":"horizontal"}] ce:["$","$Lc8",null,{"orientation":"horizontal"}] d0:["$","$Lc8",null,{"orientation":"horizontal"}] d5:["$","$Lc8",null,{"orientation":"horizontal"}] e0:["$","$Lc8",null,{"orientation":"horizontal"}] e2:["$","$Lc8",null,{"orientation":"horizontal"}] e4:["$","$Lc8",null,{"orientation":"horizontal"}] e6:["$","$Lc8",null,{"orientation":"horizontal"}] e8:["$","$Lc8",null,{"orientation":"horizontal"}] ea:["$","$Lc8",null,{"orientation":"horizontal"}] ed:["$","$Lc8",null,{"orientation":"horizontal"}] ef:["$","$Lc8",null,{"orientation":"horizontal"}] f1:["$","$Lc8",null,{"orientation":"horizontal"}] f3:["$","$Lc8",null,{"orientation":"horizontal"}] 36:o3a,2c:C 2a:C 2b:C 23:C 25:C 26:C 27:C 28:C 2e:false 2d:77080 36:C 9b:Tab0,

z_2 = x_2 + iy_2

72:["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$9b"}}]}] 9d:T1504,

z_1 \times z_2 = (x_1 + iy_1)(x_2 + iy_2)

73:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L9c",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$9d"}}]}],"$L9e"]}]}],"$L9f","$La0"]}] a1:T454,

i^2 = -1

74:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Remember that ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$a1"}}]}],", so we can substitute:"]}] a2:T19f0,

= (x_1x_2 + ix_1y_2) + (ix_2y_1 + (-1)y_1y_2)

75:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-compact","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L9c",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$a2"}}]}],"$La3"]}]}],"$La4"]}] 76:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"Now, let's group the real and imaginary parts:"}] a5:T1933,

= (x_1x_2 - y_1y_2) + (ix_1y_2 + ix_2y_1)

77:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-compact","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L9c",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$a5"}}]}],"$La6"]}]}],"$La7"]}] 78:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"So, the general formula for complex number multiplication is:"}] a8:T1f2b,

z_1 \times z_2 = (x_1x_2 - y_1y_2) + i(x_1y_2 + x_2y_1)

79:["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L9c",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$a8"}}]}],"$La9"]}]}] 7a:["$","h2",null,{"className":"mt-10 mb-6 flex scroll-mt-44 items-center font-medium tracking-tight first:mt-0 last:mb-0 text-2xl","id":"calculation-example","children":["$","a",null,{"aria-label":"Link to Calculation Example","className":"group/heading inline-flex items-center gap-4","href":"#calculation-example","title":"Calculation Example","children":[["$","span",null,{"className":"text-pretty","children":"Calculation Example"}],["$","div",null,{"className":"rounded-sm border p-2 opacity-0 transition-opacity ease-out group-hover/heading:opacity-100","children":["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0 text-muted-foreground","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M13.5 17H17C19.7614 17 22 14.7614 22 12C22 9.23858 19.7614 7 17 7H13.5M10.5 17H7C4.23858 17 2 14.7614 2 12C2 9.23858 4.23858 7 7 7H10.5","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}],["$","path","1",{"d":"M9 12H15","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}]]}]}]]}]}] aa:T613,

z_1 = 2+i

ab:T63d,

z_2 = 1-2i

7b:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Let ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$aa"}}]}]," and ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$ab"}}]}],". Find ","$Lac","."]}] 7c:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["$","strong",null,{"className":"font-medium","children":"Solution:"}]}] 7d:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"Using the distributive property:"}] ad:Tc20,

z_1 \times z_2 = (2+i)(1-2i)

7e:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-spacious","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L9c",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$ad"}}]}],"$Lae"]}]}],"$Laf","$Lb0","$Lb1","$Lb2","$Lb3","$Lb4"]}] b5:T10f2,

x_1 = 2, y_1 = 1, x_2 = 1, y_2 = -2

7f:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Or using the general formula with ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$b5"}}]}],":"]}] b6:T1f2b,

z_1 \times z_2 = (x_1x_2 - y_1y_2) + i(x_1y_2 + x_2y_1)

80:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-spacious","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L9c",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$b6"}}]}],"$Lb7"]}]}],"$Lb8","$Lb9","$Lba","$Lbb"]}] 81:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"The result is the same!"}] bc:T613,

z_1 = 2+i

bd:T63d,

z_2 = 1-2i

82:["$","div",null,{"className":"flex flex-col gap-6 rounded-xl border bg-card py-6 text-card-foreground shadow-sm content-auto-card","data-slot":"card","children":[["$","div",null,{"className":"@container/card-header grid auto-rows-min grid-rows-[auto_auto] items-start gap-2 px-6 has-data-[slot=card-action]:grid-cols-[1fr_auto] [.border-b]:pb-6","data-slot":"card-header","children":[["$","div",null,{"className":"font-medium leading-tight","data-slot":"card-title","children":"Visualization of Complex Number Multiplication"}],["$","div",null,{"className":"text-muted-foreground text-sm","data-slot":"card-description","children":["Visualization of ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$bc"}}]}],","," ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$bd"}}]}],", and their product"," ","$Lbe","."]}]]}],"$Lbf"]}] 83:["$","h2",null,{"className":"mt-10 mb-6 flex scroll-mt-44 items-center font-medium tracking-tight first:mt-0 last:mb-0 text-2xl","id":"exercise","children":["$","a",null,{"aria-label":"Link to Exercise","className":"group/heading inline-flex items-center gap-4","href":"#exercise","title":"Exercise","children":[["$","span",null,{"className":"text-pretty","children":"Exercise"}],["$","div",null,{"className":"rounded-sm border p-2 opacity-0 transition-opacity ease-out group-hover/heading:opacity-100","children":["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0 text-muted-foreground","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M13.5 17H17C19.7614 17 22 14.7614 22 12C22 9.23858 19.7614 7 17 7H13.5M10.5 17H7C4.23858 17 2 14.7614 2 12C2 9.23858 4.23858 7 7 7H10.5","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}],["$","path","1",{"d":"M9 12H15","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}]]}]}]]}]}] c0:T613,

z_1 = 1+i

c1:T9ed,

z_2 = \frac{1}{2} - 2i

84:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Let ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$c0"}}]}]," and ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$c1"}}]}],". Find ","$Lc2","."]}] 85:["$","h3",null,{"className":"mt-10 mb-6 flex scroll-mt-44 items-center font-medium tracking-tight first:mt-0 last:mb-0 text-xl","id":"answer-key","children":["$","a",null,{"aria-label":"Link to Answer Key","className":"group/heading inline-flex items-center gap-4","href":"#answer-key","title":"Answer Key","children":[["$","span",null,{"className":"text-pretty","children":"Answer Key"}],["$","div",null,{"className":"rounded-sm border p-2 opacity-0 transition-opacity ease-out group-hover/heading:opacity-100","children":["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0 text-muted-foreground","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M13.5 17H17C19.7614 17 22 14.7614 22 12C22 9.23858 19.7614 7 17 7H13.5M10.5 17H7C4.23858 17 2 14.7614 2 12C2 9.23858 4.23858 7 7 7H10.5","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}],["$","path","1",{"d":"M9 12H15","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2}]]}]}]]}]}] 86:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":"Using the distributive property:"}] c3:Tf51,

z_1 \times z_2 = (1+i)(\frac{1}{2} - 2i)

87:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-spacious","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L9c",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$c3"}}]}],"$Lc4"]}]}],"$Lc5","$Lc6","$Lc7","$Lc8","$Lc9","$Lca","$Lcb"]}] cc:T14a0,

x_1 = 1, y_1 = 1, x_2 = \frac{1}{2}, y_2 = -2

88:["$","p",null,{"className":"my-4 text-pretty tabular-nums leading-relaxed first:mt-0 last:mb-0","children":["Using the general formula with ",["$","span",null,{"data-markdown-ignore":"","children":["$","span",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$cc"}}]}],":"]}] cd:T1f2b,

z_1 \times z_2 = (x_1x_2 - y_1y_2) + i(x_1y_2 + x_2y_1)

89:["$","div",null,{"className":"my-4 space-y-0 last:mb-0 *:data-math-block:rounded-none *:data-math-block:border-b-0 [&>[data-math-block]:first-child]:rounded-t-xl [&>[data-math-block]:last-child]:rounded-b-xl [&>[data-math-block]:last-child]:border-b content-auto-math-stack-spacious","children":[["$","div",null,{"className":"overflow-hidden rounded-xl border bg-card text-card-foreground content-auto-formula","data-markdown-ignore":"","data-math-block":"","children":["$","$L9c",null,{"className":"grid","children":[["$","div",null,{"className":"px-4","children":["$","div",null,{"data-testid":"react-katex","dangerouslySetInnerHTML":{"__html":"$cd"}}]}],"$Lce"]}]}],"$Lcf","$Ld0","$Ld1","$Ld2","$Ld3"]}] 6b:["$","nav",null,{"aria-label":"Pagination navigation","className":"mt-10 pt-10","children":["$","div",null,{"className":"mx-auto grid max-w-3xl gap-6 px-6 sm:grid-cols-2","children":[["$","$Ld4",null,{"className":"group flex h-auto flex-col whitespace-normal py-3 shadow-xs items-start","nativeButton":false,"render":["$","$L4e",null,{"href":"/en/subjects/mathematics/complex-number/modulus-argument-complex-numbers?ctx=merdeka~class-11-mathematics-complex-number","title":"Modulus and Argument of Complex Numbers","children":[["$","div",null,{"className":"flex items-center gap-2 font-normal text-muted-foreground text-sm transition-colors group-hover:text-accent-foreground","children":[["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M5.5 12.002H19","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M10.9999 18.002C10.9999 18.002 4.99998 13.583 4.99997 12.0019C4.99996 10.4208 11 6.00195 11 6.00195","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}]]}],"Previous",false]}],["$","p",null,{"className":"w-full text-foreground transition-colors group-hover:text-accent-foreground","children":"Modulus and Argument of Complex Numbers"}]]}],"variant":"outline"}],["$","$Ld4",null,{"className":"group flex h-auto flex-col whitespace-normal py-3 shadow-xs items-end","nativeButton":false,"render":["$","$L4e",null,{"href":"/en/subjects/mathematics/complex-number/principal-argument-complex-numbers?ctx=merdeka~class-11-mathematics-complex-number","title":"Principal Argument of Complex Numbers","children":[["$","div",null,{"className":"flex items-center gap-2 font-normal text-muted-foreground text-sm transition-colors group-hover:text-accent-foreground","children":[false,"Next",["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M18.5 12L4.99997 12","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M13 18C13 18 19 13.5811 19 12C19 10.4188 13 6 13 6","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}]]}]]}],["$","p",null,{"className":"w-full text-foreground transition-colors group-hover:text-accent-foreground text-right","children":"Principal Argument of Complex Numbers"}]]}],"variant":"outline"}]]}]}] 98:["$","$L91",null,{"children":["$","$L92",null,{"render":["$","a",null,{"aria-label":"Report","href":"https://github.com/nakafaai/nakafa.com/issues/new/choose","rel":"noopener noreferrer","target":"_blank","title":"Report","children":[["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M3.01206 6.59744C2.89214 7.65674 3.6584 10.1951 5.87693 10.255","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M18.2891 10.195C19.3684 10.255 20.9873 8.99582 20.9873 6.59741","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","2",{"d":"M20.0876 20.9879C20.1476 19.6088 19.2482 17.4742 17.5093 17.4142","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","3",{"d":"M3.90138 20.9881C3.84009 19.5998 4.7594 17.4509 6.53675 17.3905","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","4",{"d":"M3.01227 13.7926H5.21757","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","5",{"d":"M21 13.7926L18.8282 13.7926","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","6",{"d":"M11.9932 13.7926V10.8546M16.4902 2.99982L14.6914 4.79862M7.49615 2.99982L9.29496 4.79862","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","7",{"d":"M6.95612 8.61209C8.57504 9.77532 12.5924 11.4542 16.9695 8.68404","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","8",{"d":"M16.826 7.6767C13.2523 2.7 8.69536 5.09841 7.07644 7.8206C6.02093 9.59542 4.37823 13.8886 7.49616 18.5655C10.8539 22.6667 14.8113 20.808 16.4302 18.6494C17.9892 16.7906 19.5242 11.9938 16.826 7.6767Z","stroke":"currentColor","strokeLinecap":"round","strokeWidth":2,"opacity":"$undefined"}]]}],["$","span",null,{"className":"truncate","children":"Report"}],["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"ml-auto size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M11.0991 3.00012C7.45013 3.00669 5.53932 3.09629 4.31817 4.31764C3.00034 5.63568 3.00034 7.75704 3.00034 11.9997C3.00034 16.2424 3.00034 18.3638 4.31817 19.6818C5.63599 20.9999 7.75701 20.9999 11.9991 20.9999C16.241 20.9999 18.3621 20.9999 19.6799 19.6818C20.901 18.4605 20.9906 16.5493 20.9972 12.8998","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M20.556 3.49612L11.0487 13.0586M20.556 3.49612C20.062 3.00151 16.7343 3.04761 16.0308 3.05762M20.556 3.49612C21.05 3.99074 21.0039 7.32273 20.9939 8.02714","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}]]}]]}],"tooltip":"Report"}]}] 99:["$","$L91",null,{"children":["$","$L92",null,{"render":["$","a",null,{"aria-label":"Source code","href":"https://github.com/nakafaai/aksara/blob/a48d644c809419c93dc247239eabba9ced519051/packages/corpus/material/lesson/mathematics/complex-number/multiplication-complex-numbers/en.mdx","rel":"noopener noreferrer","target":"_blank","title":"Source code","children":[["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M10 20.5675C6.57143 21.7248 3.71429 20.5675 2 17","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M10 22V18.7579C10 18.1596 10.1839 17.6396 10.4804 17.1699C10.6838 16.8476 10.5445 16.3904 10.1771 16.2894C7.13394 15.4528 5 14.1077 5 9.64606C5 8.48611 5.38005 7.39556 6.04811 6.4464C6.21437 6.21018 6.29749 6.09208 6.31748 5.9851C6.33746 5.87813 6.30272 5.73852 6.23322 5.45932C5.95038 4.32292 5.96871 3.11619 6.39322 2.02823C6.39322 2.02823 7.27042 1.74242 9.26698 2.98969C9.72282 3.27447 9.95075 3.41686 10.1515 3.44871C10.3522 3.48056 10.6206 3.41384 11.1573 3.28041C11.8913 3.09795 12.6476 3 13.5 3C14.3524 3 15.1087 3.09795 15.8427 3.28041C16.3794 3.41384 16.6478 3.48056 16.8485 3.44871C17.0493 3.41686 17.2772 3.27447 17.733 2.98969C19.7296 1.74242 20.6068 2.02823 20.6068 2.02823C21.0313 3.11619 21.0496 4.32292 20.7668 5.45932C20.6973 5.73852 20.6625 5.87813 20.6825 5.9851C20.7025 6.09207 20.7856 6.21019 20.9519 6.4464C21.6199 7.39556 22 8.48611 22 9.64606C22 14.1077 19.8661 15.4528 16.8229 16.2894C16.4555 16.3904 16.3162 16.8476 16.5196 17.1699C16.8161 17.6396 17 18.1596 17 18.7579V22","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}]]}],["$","span",null,{"className":"truncate","children":"Source code"}],["$","svg",null,{"ref":"$undefined","xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"viewBox":"0 0 24 24","fill":"none","color":"currentColor","className":"ml-auto size-4 shrink-0","strokeWidth":2,"stroke":"currentColor","children":[["$","path","0",{"d":"M11.0991 3.00012C7.45013 3.00669 5.53932 3.09629 4.31817 4.31764C3.00034 5.63568 3.00034 7.75704 3.00034 11.9997C3.00034 16.2424 3.00034 18.3638 4.31817 19.6818C5.63599 20.9999 7.75701 20.9999 11.9991 20.9999C16.241 20.9999 18.3621 20.9999 19.6799 19.6818C20.901 18.4605 20.9906 16.5493 20.9972 12.8998","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}],["$","path","1",{"d":"M20.556 3.49612L11.0487 13.0586M20.556 3.49612C20.062 3.00151 16.7343 3.04761 16.0308 3.05762M20.556 3.49612C21.05 3.99074 21.0039 7.32273 20.9939 8.02714","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"opacity":"$undefined"}]]}]]}],"tooltip":"Source code"}]}]