Number Attributes and Methods

# Creating a complex numberc = 2 + 3j# Accessing real attribute (real part)print(c.real)  # Output: 2.0# Accessing imag attribute (imaginary part)print(c.imag)  # Output: 3.0# Calling conjugate() method to get conjugateprint(c.conjugate())  # Output: (2-3j)

# Viewing number data typesprint(type(42))        # Output: <class 'int'>print(type(3.14))      # Output: <class 'float'>print(type(2+3j))      # Output: <class 'complex'>

# Example usage of real attributez1 = 4 + 5jz2 = -2 + 7jz3 = 10 + 0j  # Pure real numberprint(f"Real part of {z1} is {z1.real}")print(f"Real part of {z2} is {z2.real}")print(f"Real part of {z3} is {z3.real}")# Output:# Real part of (4+5j) is 4.0# Real part of (-2+7j) is -2.0# Real part of (10+0j) is 10.0

# Example usage of imag attributez1 = 3 + 8jz2 = 6 - 4jz3 = 0 + 9j  # Pure imaginary numberprint(f"Imaginary part of {z1} is {z1.imag}")print(f"Imaginary part of {z2} is {z2.imag}")print(f"Imaginary part of {z3} is {z3.imag}")# Output:# Imaginary part of (3+8j) is 8.0# Imaginary part of (6-4j) is -4.0# Imaginary part of 9j is 9.0

# Example usage of conjugate() methodz1 = 3 + 4jz2 = -2 - 5jz3 = 7 + 0jprint(f"Conjugate of {z1} is {z1.conjugate()}")print(f"Conjugate of {z2} is {z2.conjugate()}")print(f"Conjugate of {z3} is {z3.conjugate()}")# Output:# Conjugate of (3+4j) is (3-4j)# Conjugate of (-2-5j) is (-2+5j)# Conjugate of (7+0j) is (7-0j)

import math# Calculating complex number modulus using conjugatez = 3 + 4jmodulus_squared = z * z.conjugate()modulus = math.sqrt(modulus_squared.real)print(f"Complex number: {z}")print(f"Its conjugate: {z.conjugate()}")print(f"z × z*: {modulus_squared}")print(f"Modulus |z|: {modulus}")# Output:# Complex number: (3+4j)# Its conjugate: (3-4j)# z × z*: (25+0j)# Modulus |z|: 5.0

# Some methods on integer numbersn = 42# bit_length() method - calculates the number of bits neededprint(f"Number of bits for {n}: {n.bit_length()}")# to_bytes() method - converts to bytesbyte_representation = n.to_bytes(2, byteorder='big')print(f"Byte representation of {n}: {byte_representation}")# Output:# Number of bits for 42: 6# Byte representation of 42: b'\x00*'

# Some methods on float numbersf = 3.14159# is_integer() method - checks if float is a whole numberprint(f"{f} is a whole number: {f.is_integer()}")print(f"{4.0} is a whole number: {(4.0).is_integer()}")# as_integer_ratio() method - returns ratio as a fractionratio = f.as_integer_ratio()print(f"Ratio of {f}: {ratio}")# Output:# 3.14159 is a whole number: False# 4.0 is a whole number: True# Ratio of 3.14159: (3537115888337719, 1125899906842624)

def validate_complex_input(z):  """Function to validate complex number input"""  if not isinstance(z, complex):      return False, "Input is not a complex number"    if z.real < 0:      return False, "Real part cannot be negative"    if z.imag == 0:      return False, "Imaginary part cannot be zero"    return True, "Valid input"# Testing validation functiontest_numbers = [3+4j, -2+5j, 7+0j, 2.5+1.5j]for num in test_numbers:  is_valid, message = validate_complex_input(num)  print(f"{num}: {message}")

def complex_operations(z1, z2):  """Performing various operations on complex numbers"""  print(f"Number 1: {z1}")  print(f"Number 2: {z2}")  print(f"Real part of z1: {z1.real}")  print(f"Imaginary part of z1: {z1.imag}")  print(f"Conjugate of z1: {z1.conjugate()}")    # Mathematical operations  addition = z1 + z2  multiplication = z1 * z2.conjugate()    print(f"z1 + z2 = {addition}")  print(f"z1 × z2* = {multiplication}")# Usage examplez1 = 2 + 3jz2 = 1 - 2jcomplex_operations(z1, z2)