In this tutorial, we will look at how to convert a complex number in Python to its polar form with the help of some examples. In the polar form, a complex number is represented using its magnitude (or absolute value) and its phase angle.

## How to get the polar coordinates of a complex number in Python?

To get the polar form of a complex number in Python, use the `numpy.abs()`

function to get its magnitude and the `numpy.angle()`

function to get its phase angle.

Let’s write a custom function in Python, to return the polar form for a complex number as the `(magnitude, phase angle)`

tuple.

import numpy as np # function to get polar form of complex number def get_polar_form(z): # magnitude mag = np.abs(z) # phase angle in radians phase = np.angle(z) return (mag, phase)

Here, we use the `numpy.abs()`

function to calculate the magnitude (or the absolute value) of the complex number and the `numpy.angle()`

function to get its phase angle.

## Examples

Let’s now look at examples of using the above function on complex numbers.

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import numpy as np # function to get polar form of complex number def get_polar_form(z): # magnitude mag = np.abs(z) # phase angle in radians phase = np.angle(z) return (mag, phase) # get the polar form of complex number get_polar_form(3+4j)

Output:

(5.0, 0.9272952180016122)

Here, we used the `get_polar_form()`

custom function to get the polar form for the complex number `3 + 4j`

. You can see that its magnitude is 5 units and its phase angle is approx. 0.927 radians.

Note that the `numpy.angle()`

function returns the phase angle in radians by default.

To get the phase angle in degrees, pass `deg=True`

as an argument to the `numpy.angle()`

function.

# function to get polar form of complex number def get_polar_form(z): # magnitude mag = np.abs(z) # phase angle in degrees phase = np.angle(z, deg=True) return (mag, phase) # get the polar form of complex number get_polar_form(3+4j)

Output:

(5.0, 53.13010235415598)

We get the complex number in polar form with the angle in degrees.

Let’s apply the above function to some other values – a real number, a complex number with non-zero real and imaginary parts, and an imaginary number.

# get the polar form of complex number print(get_polar_form(14)) print(get_polar_form(1+1j)) print(get_polar_form(-5j))

Output:

(14, 0.0) (1.4142135623730951, 45.0) (5.0, -90.0)

We get the polar form for each of the above inputs. You can see that for the real number 14, the phase angle is 0 whereas for the imaginary input -5j, the phase angle is -90 degrees.

## Summary

In this tutorial, we looked at how we can use a combination of the `numpy.abs()`

and `numpy.angle()`

functions to construct the polar form of a complex number in Python.

You might also be interested in –

- Practical Guide to Working with Complex Numbers in Python
- Python – Add Two Complex Numbers
- Python – Subtract Two Complex Numbers
- Python – Multiply Two Complex Numbers
- Python – Divide Two Complex Numbers
- Python – Generate a Random Complex Number
- Python – Get the Phase Angle of a Complex Number
- Python – Get the Absolute Value of a Complex Number
- Numpy – Get the Complex Conjugate
- Numpy – Get the Real Part of a Complex Number
- Numpy – Get the Imaginary Part of a Complex Number
- Numpy – Check If a Number is Real
- Numpy – Check If a Number is Complex