How to use cmath module In Python
Python’s cmath module provides access to the mathematical functions for complex numbers. It contains several functions that are used for converting coordinates from one domain to another.
Out of them, some are explained as:
1. cmath.polar(x):
Return the representation of x in polar coordinates. cmath.polar() function is used to convert a complex number to polar coordinates.
Python3
# Python code to implement# the polar()function# importing "cmath"# for mathematical operationsimport cmath# using cmath.polar() methodnum = cmath.polar(1)print(num) |
Output
(1.0, 0.0)
Time Complexity: O(1)
Auxiliary space: O(1)
2. cmath.phase (z): This method returns the phase of the complex number z(also known as the argument of z).
Python3
import cmathx = -1.0y = 0.0z = complex(x, y)# printing phase of a complex number using phase()print("The phase of complex number is : ", end="")print(cmath.phase(z)) |
Output
The phase of complex number is : 3.141592653589793
Python Program to convert complex numbers to Polar coordinates
Before starting with the program, let’s see the basics of Polar Coordinates and then use Python’s cmath and abs module to convert it. Polar coordinates are just a different way of representing Cartesian coordinates or Complex Numbers. A complex number z is defined as :
It is completely determined by its real part x and imaginary part y. Here, j is the imaginary unit.
The polar coordinates (r , φ) is completely determined by modulus r and phase angle φ.
Where,
r: Distance from z to origin, i.e.,
r = \sqrt{x^{2}+y^{2}}
φ: Counterclockwise angle measured from the positive x-axis to the line segment that joins z to the origin.
The conversion of complex numbers to polar coordinates is explained below with examples.
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