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Python – Get the Phase Angle of a Complex Number

In this tutorial, we will look at how to get the phase (or the angle) of a complex number in Python with the help of some examples. The phase (or angle) of a complex number is defined as the angle the complex number vector makes with the real axis in the counter-clockwise direction.

How to get the phase of a complex number in Python?

phase angle of a complex number python

You can use the numpy.angle() function to get the phase (or the angle) of a complex number in Python. The following is the syntax –

# get the angle of complex number - make sure to import numpy
numpy.angle(z, deg=False)

It returns the angle in radians by default. If you want to get the angle in degrees, pass deg=True as an argument to the function.

Note that you can use this function on an array of complex numbers as well. In which case it will return an array of the element-wise angle values for the complex numbers in the array.

Examples

Let’s now look at some examples of using the numpy.angle() function.

Example 1 – Get the phase of a complex number in radians

By default, the numpy.angle() function returns the phase angle in radians.

Let’s apply it to three scalar values – a real number, a complex number with non-zero real and imaginary components, and a complex number with a non-zero imaginary component (an imaginary number).

import numpy as np

# get the angle of complex number (in radians)
print(np.angle(14))
print(np.angle(1+1j))
print(np.angle(3j))

Output:

0.0
0.7853981633974483
1.5707963267948966

We get the angles for each of the complex numbers in radians.

Example 2 – Get the phase of a complex number in degrees

To get the phase of a complex number in degrees, pass deg=True as an argument to the numpy.angle() function.

Let’s use the same three inputs as the above example.

# get the angle of complex number (in degrees)
print(np.angle(14, deg=True))
print(np.angle(1+1j, deg=True))
print(np.angle(3j, deg=True))

Output:

0.0
45.0
90.0

We get the angles of the complex numbers in degrees.

Example 3 – Get the phase of an array of complex numbers

You can also apply the numpy.angle() function to an array, in which case, it will return a Numpy array of the element-wise phase angles.

Let’s apply this function on a Numpy array.

# element-wise get the angle in array of complex numbers
ar = np.array([14, 1+1j, 3j])
np.angle(ar, deg=True)

Output:

array([ 0., 45., 90.])

We get the element-wise array of the angles for the values in the ar array.

Summary

In this tutorial, we looked at how we can use the numpy.angle() function to get the phase (or angle) of a complex number in Python. The following are the key takeaways from this tutorial.

  • The numpy.angle() function returns the angle of a complex number in radians by default.
  • To get the angle in degrees, pass deg=True to the numpy.angle() function.
  • You can also apply this function on an array, in which case it will return the element-wise angles.

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Author

  • Piyush

    Piyush is a data scientist passionate about using data to understand things better and make informed decisions. In the past, he's worked as a Data Scientist for ZS and holds an engineering degree from IIT Roorkee. His hobbies include watching cricket, reading, and working on side projects.