# How to get the modulus of complex number in python ?

Daidalos November 15, 2019

Examples of how to get the modulus of complex number in python:

### Definition

The modulus of complex number $z=a+ib$ is:

|z| = |a+ib| = \sqrt{a^2+b^2}

with $a$ and $b$ are the real and imaginary parts.

### Create a function to calculate the modulus of complex number

To calculate the modulus of complex number a solution is to define a simple python function:

>>> import math
>>> def complexe_modulo(z):
...     a = z.real
...     b = z.imag
...     return math.sqrt(a**2+b**2)
...


So for example with the complex number

>>> z = 1 + 1.j


the function defined above returns:

>>> complexe_modulo(z)
1.4142135623730951


### Using the built-in function abs()

Another solution is to use the function abs(). For example with the complex number

>>> z = 1 + 1.j
>>> z
(1+1j)


the function abs() returns:

>>> abs(z)
1.4142135623730951


### Matrix of complex numbers

Example with a complex number matrix:

>>> import numpy as np
>>> Z = np.array([[1+2j,1+3j],[5+6j,3+8j]])
>>> Z
array([[ 1.+2.j,  1.+3.j],
       [ 5.+6.j,  3.+8.j]])
>>> np.abs(Z)
array([[ 2.23606798,  3.16227766],
       [ 7.81024968,  8.54400375]])


### References

Complex modulus wikipedia
numpy.absolute doc scipy
Most memory-efficient way to compute abs()**2 of complex numpy ndarray stackoverflow

Licence