5 Best Ways to Return the Angle of the Complex Argument in Degrees in Python

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πŸ’‘ Problem Formulation: Given a complex number in Python, it’s often necessary to determine its phase, or argument, which refers to the angle in degrees between the positive real axis and the line representing the complex number. This can be particularly useful in fields like electrical engineering or physics. For instance, if the input is 1 + 1j, the desired output would be the angle in degrees, approximately 45 degrees.

Method 1: Using cmath.phase() and math.degrees()

This method involves the standard library’s cmath module to compute the phase of the complex number, which returns the angle in radians. To convert this to degrees, we use the math.degrees() function. This is a straightforward approach when dealing with complex numbers in Python.

Here’s an example:

import cmath
import math

complex_num = 1 + 1j
angle_in_radians = cmath.phase(complex_num)
angle_in_degrees = math.degrees(angle_in_radians)
print(angle_in_degrees)

Output: 45.0

This code snippet calculates the argument of a complex number 1 + 1j. The angle is initially in radians from the cmath.phase() function, and it’s converted to degrees with math.degrees(). The output is the angle in degrees, which is 45.0 for this example.

Method 2: Using numpy.angle() with degrees=True

For those utilizing the popular numpy library, it offers an angle function that can directly return the angle in degrees. By setting the deg parameter to True, the angle will be computed in degrees. This is an efficient way especially if you are already working with numpy arrays.

Here’s an example:

import numpy as np

complex_num = 1 + 1j
angle_in_degrees = np.angle(complex_num, deg=True)
print(angle_in_degrees)

Output: 45.0

This snippet shows how to get the argument of the complex number using numpy.angle(). By setting deg=True, we instruct the function to return the result directly in degrees. The output, similarly, is 45.0 degrees for the complex number 1 + 1j.

Method 3: Using math.atan2()

Another method is to use the math.atan2() function, which computes the arctangent of y/x considering two arguments, y and x, hence accounting for the correct quadrant of the angle. We need to pass the imaginary part as y and the real part as x, and then convert the result to degrees.

Here’s an example:

import math

complex_num = 1 + 1j
angle_in_radians = math.atan2(complex_num.imag, complex_num.real)
angle_in_degrees = math.degrees(angle_in_radians)
print(angle_in_degrees)

Output: 45.0

The math.atan2() function provides the phase of the complex number directly considering its quadrants. The result is then converted to degrees by math.degrees(). It’s a reliable method especially if your project does not require importing additional libraries like cmath or numpy.

Method 4: Using a Custom Function

Creating a custom function can be useful for understanding the mathematics behind the angle calculation. Using math.atan2() and math.degrees(), we can roll this into a reusable function designed specifically for converting complex numbers to their angle representation in degrees.

Here’s an example:

import math

def complex_angle_in_degrees(complex_num):
    return math.degrees(math.atan2(complex_num.imag, complex_num.real))
    
complex_num = 1 + 1j
angle_in_degrees = complex_angle_in_degrees(complex_num)
print(angle_in_degrees)

Output: 45.0

This custom function, complex_angle_in_degrees, combines the math.atan2() and math.degrees() methods to calculate the angle of a complex number in degrees. This modular approach makes the code cleaner and more maintainable especially if this operation needs to be repeated throughout the codebase.

Bonus One-Liner Method 5: Using Lambda Functions

For a quick and concise one-liner, Python’s lambda functions can be used to calculate the angle directly within the print function. This method is best suited for situations where a quick calculation is needed without creating a full function.

Here’s an example:

import cmath
import math

complex_num = 1 + 1j
print((lambda x: math.degrees(cmath.phase(x)))(complex_num))

Output: 45.0

Here a lambda function is created on the fly to compute the angle of a complex number in degrees. It’s a brief way to perform the calculation within a single line of code, which might be convenient for simple scripts or interactive sessions.

Summary/Discussion

  • Method 1: Using cmath.phase() and math.degrees(). This is a straightforward approach that is ready to use without any additional libraries. The downside is it requires two function calls.
  • Method 2: Using numpy.angle() with deg=True. This is efficient especially in the context of numpy array operations, but it requires the numpy library, which might be substantial for simple needs.
  • Method 3: Using math.atan2(). It uses basic functions from the math module and is reliable without external dependencies, but requires manual handling of the output to convert from radians to degrees.
  • Method 4: Using a Custom Function. Great for reuse across a codebase and encapsulates functionality in a clean and understandable way. However, you need to define and maintain this custom code yourself.
  • Method 5: Using a Lambda Function. Ideal for quick, on-the-spot calculations without creating discrete functions. However, lambda functions can decrease code readability if overused or used in complex operations.