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

### Definition

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

\begin{equation}

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

\end{equation}

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

Links | Site |
---|---|

Complex modulus | wikipedia |

numpy.absolute | doc scipy |

Most memory-efficient way to compute abs()**2 of complex numpy ndarray | stackoverflow |