Complex Numbers in Python | Set 1 (Introduction)

Last Updated : 21 Aug, 2024

Not only real numbers, Python can also handle complex numbers and its associated functions using the file "cmath". Complex numbers have their uses in many applications related to mathematics and python provides useful tools to handle and manipulate them. Converting real numbers to complex number An complex number is represented by " x + yi ". Python converts the real numbers x and y into complex using the function complex(x,y). The real part can be accessed using the function real() and imaginary part can be represented by imag().

Python

# Python code to demonstrate the working of
# complex(), real() and imag()

# importing "cmath" for complex number operations
import cmath

# Initializing real numbers
x = 5
y = 3

# converting x and y into complex number
z = complex(x, y)

# printing real and imaginary part of complex number
print("The real part of complex number is:", z.real)
print("The imaginary part of complex number is:", z.imag)

Output

The real part of complex number is: 5.0
The imaginary part of complex number is: 3.0

An alternative way to initialize a complex number

Below is the implementation of how can we make complex no. without using complex() function.

Python

# An alternative way to initialize complex numbers"
# importing "cmath" for complex number operations
import cmath

# Initializing complex number
z = 5+3j
# Print the parts of Complex No.
print("The real part of complex number is : ", end="")
print(z.real)

print("The imaginary part of complex number is : ", end="")
print(z.imag)

Output

The real part of complex number is : 5.0
The imaginary part of complex number is : 3.0

Explanation: Phase of complex number Geometrically, the phase of a complex number is the angle between the positive real axis and the vector representing a complex number. This is also known as the argument of a complex number. Phase is returned using phase(), which takes a complex number as an argument. The range of phase lies from -pi to +pi. i.e from -3.14 to +3.14.

Python

# importing "cmath" for complex number operations
import cmath

# Initializing real numbers
x = -1.0
y = 0.0

# converting x and y into complex number
z = complex(x, y)

# printing phase of a complex number using phase()
print("The phase of complex number is:", cmath.phase(z))

Output

The phase of complex number is: 3.141592653589793

Converting from polar to rectangular form and vice versa Conversion to polar is done using polar(), which returns a pair(r,ph) denoting the modulus r and phase angle ph. modulus can be displayed using abs() and phase using phase(). A complex number converts into rectangular coordinates by using rect(r, ph), where r is modulus and ph is phase angle. It returns a value numerically equal to r * (math.cos(ph) + math.sin(ph)*1j)

Python

# importing "cmath" for complex number operations
import cmath
import math

# Initializing real numbers
x = 1.0
y = 1.0

# converting x and y into complex number
z = complex(x, y)

# converting complex number into polar using polar()
w = cmath.polar(z)

# printing modulus and argument of polar complex number
print("The modulus and argument of polar complex number is:", w)

# converting complex number into rectangular using rect()
w = cmath.rect(1.4142135623730951, 0.7853981633974483)

# printing rectangular form of complex number
print("The rectangular form of complex number is:", w)

Output

The modulus and argument of polar complex number is: (1.4142135623730951, 0.7853981633974483)
The rectangular form of complex number is: (1.0000000000000002+1j)

Complex Numbers in Python | Set 2 (Important Functions and Constants)