**π‘ 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.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.