Complex Numbers in Python | Kit 1 (Introduction)



Converting real numbers to complex numbers

A complex number is represented as “ x + yi “. Python converts real numbers x and y to a complex using the complex (x, y) function. The real part can be accessed using the real () function, and the imaginary part can be represented by imag () .

# Python code to demonstrate how it works
# complex (), real () and imag ()

 
# import & quot; cmath & quot; for operations with complex numbers

import cmath

 
# Initializing real numbers

x = 5

y = 3

 
# convert x and y to complex number

z = complex (x, y); 

 
# printing real and imaginary parts of a complex number

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  

Complex phase th number

Geometrically, the phase of a complex number — it is the angle between the positive real axis and the vector representing the complex number . This is also known as the argument of a complex number. Phase is returned by phase () , which takes a complex number as an argument. The phase range is from -pi to + pi. that is, from -3.14 to +3.14 .

# Python code to demonstrate how it works
# phase ()

 
# import & quot; cmath & quot; for operations with complex numbers

import cmath

 
# Initializing real numbers

x = - 1.0

y = 0.0

 
# convert x and y to complex number

z = complex (x, y); 

 
# printing the phase of a complex number using phase ()

print ( "The phase of complex number is:" , end = "")

print (cmath.phase (z))

Output:

 The phase of complex number is: 3.141592653589793 

Conversion from polar to rectangular and vice versa

Conversion to polar is performed using polar () , which returns a pair (r, ph), denoting module r and phase angle ph . a module can be rendered using abs (), and a phase using phase ()
A complex number is converted to rectangular coordinates using rect (r, ph) , where r — module, and ph — phase angle . Returns a value numerically r * (math.cos (ph) + math.sin (ph) * 1j)

# Python code to demonstrate how it works
# polar () and rect ()

 
# import & quot; cmath & quot; for operations with complex numbers

import cmath

import math

 
# Initializing real numbers

x = 1.0

y = 1.0

  
# convert x and y to complex number

z = complex (x, y); 

 
# convert complex number to polar using polar ()

w = cmath.polar (z)

 
# print engine and polar complex number argument

print ( "The modulus and argument of polar complex number is:" , end = "")

print (w)

 
# convert complex number to rectangular using rect ()

w = cmath.rect ( 1.4142135623730951 , 0.7853981633974483 )

 
# printing a rectangular complex number

print ( "The rectangular form of complex number is:" , end = "")

print (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) 

Manjit Singh . If you are as Python.Engineering and would like to contribute, you can also write an article using contribute.python.engineering or by posting an article contribute @ python.engineering. See my article appearing on the Python.Engineering homepage and help other geeks.

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