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
