# Python – Convert Complex Number to Polar Form

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 = 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 = 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.

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## Author

• Piyush is a data professional passionate about using data to understand things better and make informed decisions. He has experience working as a Data Scientist in the consulting domain and holds an engineering degree from IIT Roorkee. His hobbies include watching cricket, reading, and working on side projects.