Python program for multiplication and division of complex number

Given two complex numbers. The task is to multiply and divide them. Multiplication of complex number: In Python complex numbers can be multiplied using * operator 
Examples:

Input: 2+3i, 4+5i 
Output: Multiplication is : (-7+22j) 

Input: 2+3i, 1+2i
Output: Multiplication is : (-4+7j) 

Python3

# Python program to demonstrate
# multiplication of complex numbers


def mulComplex( z1, z2):
    return z1*z2


# driver code
z1 = complex(2, 3)
z2 = complex(4, 5)


print("Multiplication is :", mulComplex(z1,z2))

Output:

Multiplication is : (-7+22j)

Time Complexity: O(1)

Auxiliary Space: O(1)

Division of complex number: In Python, complex numbers can be divided using the / operator. 

Examples:

Input: 2+3i, 4+5i
Output: Division  is : (0.5609756097560976+0.0487804878048781j)

Input: 2+3i, 1+2i
Output: Division is :(1.6-0.2j) 

Python3

# Python program to demonstrate
# division of complex numbers


def divComplex( z1, z2):
    return z1 / z2

# driver code

z1 = complex(2, 3)
z2 = complex(4, 5)

print( "Division is :", (divComplex(z1, z2))

Output:

Division is : (0.5609756097560976+0.0487804878048781j)

Time Complexity: O(1)

Auxiliary Space: O(1)

Approach:

Define a class ComplexNumber to represent complex numbers with real and imaginary parts.

Implement the __init__ method to initialize the real and imaginary parts of the complex number.

Implement the __repr__ method to provide a string representation of the complex number in the format a + bi.

Implement the __mul__ method to define the multiplication of two complex numbers. This is done using the formula: (a + bi) * (c + di) = (ac – bd) + (ad + bc)i.

Implement the __truediv__ method to define the division of two complex numbers. This is done using the formula: (a + bi) / (c + di) = [(ac + bd) / (c^2 + d^2)] + [(bc – ad) / (c^2 + d^2)]i.

Create two instances of the ComplexNumber class to represent the input complex numbers.

Use the * operator to multiply the two complex numbers and print the result.

Use the / operator to divide the two complex numbers and print the result.

Python3

class ComplexNumber:
    def __init__(self, real, imag):
        self.real = real
        self.imag = imag

    def __repr__(self):
        return "{}{:+}i".format(self.real, self.imag)

    def __mul__(self, other):
        real = self.real * other.real - self.imag * other.imag
        imag = self.real * other.imag + self.imag * other.real
        return ComplexNumber(real, imag)

    def __truediv__(self, other):
        denom = other.real**2 + other.imag**2
        real = (self.real * other.real + self.imag * other.imag) / denom
        imag = (self.imag * other.real - self.real * other.imag) / denom
        return ComplexNumber(real, imag)

# Sample input and output
a = ComplexNumber(2, 3)
b = ComplexNumber(4, 5)
print("Multiplication is :", a * b)

a = ComplexNumber(2, 3)
b = ComplexNumber(1, 2)
print("Multiplication is :", a * b)
print("Division is :", a / b)

Output

Multiplication is : -7+22i
Multiplication is : -4+7i
Division is : 1.6-0.2i

The time complexity of the __mul__ and __truediv__ methods is O(1), which means that they take a constant amount of time to run, regardless of the input size. 

The auxiliary space is also O(1),