# How to get a complex number in polar coordinates in python ?

Published: November 16, 2019

Examples of how to get a complex number in polar coordinates in python:

### Using the python module cmath

To get a complex number in polar coordinate a solution is to use the python module cmath:

````>>> import cmath`
```

Let's consider the following complex number:

````>>> z = 2 + 3j`
```

to get the polar coordinates:

````>>> r,theta = cmath.polar(z)`
`>>> r`
`3.605551275463989`
`>>> theta`
`0.982793723247329`
```

Note: to return the complex number in Cartesian coordinates a solution is to use the function rect():

````>>> cmath.rect(r,theta)`
`(2+2.9999999999999996j)`
```

### Calculate the phase and the modulus

Another solution is to use the functions abs():

````>>> r = abs(z)`
`>>> r`
`3.605551275463989`
```

and phase():

````>>> theta = cmath.phase(z)`
`>>> theta`
`0.982793723247329`
```

````>>> import math`
`>>> def calculate_r(z):`
`...     a = z.real`
`...     b = z.imag`
`...     return math.sqrt(a**2+b**2)`
`... `
`>>> `
`>>> `
`>>> def calculate_theta(z):`
`...     a = z.real`
`...     r = abs(z)`
`...     return math.acos(a/r)`
`... `
`>>> `
`>>> calculate_r(z)`
`3.605551275463989`
`>>> calculate_theta(z)`
`0.982793723247329`
```