**π‘ Problem Formulation:** Calculating the angle of a complex number’s argument in Python is a common task in scientific and engineering computations. The complex argument’s angle, typically represented in radians, describes the direction of the complex number in the complex plane. Given a complex number such as `3+4j`

, we aim to find its angle, which would be the output of approximately `0.927`

radians.

## Method 1: Using cmath.phase()

The `cmath.phase()`

function in Python returns the phase of a complex number, which is the angle between the real axis and the vector representing the complex number. It is part of the `cmath`

module, which provides mathematical functions for complex numbers.

Here’s an example:

import cmath complex_num = 3 + 4j angle = cmath.phase(complex_num) print(angle)

Output: `0.9272952180016122`

This code snippet imports the `cmath`

module and uses the `phase()`

function to calculate the angle of the complex number `3+4j`

. The result is the radian measure of the angle from real axis to the number in the complex plane.

## Method 2: Using math.atan2()

The `math.atan2()`

function computes the arctangent of y/x using the signs of both arguments to determine the correct quadrant. When dealing with complex numbers, this can be used by passing the imaginary part as y and the real part as x.

Here’s an example:

import math complex_num = 3 + 4j angle = math.atan2(complex_num.imag, complex_num.real) print(angle)

Output: `0.9272952180016122`

This snippet uses the standard `math`

library and its `atan2()`

function to find the angle of the complex argument. It takes the imaginary and real parts of the complex number as inputs to determine the angle to the positive x-axis.

## Method 3: Using numpy.angle()

The `numpy.angle()`

function from the NumPy library returns the angle of the complex argument. This approach is most useful when dealing with arrays of complex numbers, as NumPy is optimized for array operations.

Here’s an example:

import numpy as np complex_num = 3 + 4j angle = np.angle(complex_num) print(angle)

Output: `0.9272952180016122`

The code snippet shows how the `numpy.angle()`

function can be used to calculate the argument’s angle. This function is particularly advantageous for vectorized operations on arrays of complex numbers.

## Method 4: Using the `cmath.polar()`

Function

The function `cmath.polar()`

returns the modulus and the phase of a complex number. If one is only interested in the phase, they can disregard the modulus returned by this function.

Here’s an example:

import cmath complex_num = 3 + 4j modulus, angle = cmath.polar(complex_num) print(angle)

Output: `0.9272952180016122`

This example uses the `cmath.polar()`

function to get both modulus and phase of the complex number. However, only the phase (or angle) component is printed.

## Bonus One-Liner Method 5: Lambda Function

A lambda function can be created to encapsulate the call to the `cmath.phase()`

function in a short, concise manner.

Here’s an example:

import cmath get_angle = lambda z: cmath.phase(z) print(get_angle(3 + 4j))

Output: `0.9272952180016122`

This code snippet defines a lambda function named `get_angle`

that uses the `cmath.phase()`

function to get the angle of a given complex number. It’s a concise one-liner that can be reused throughout the code when necessary.

## Summary/Discussion

**Method 1:**Using`cmath.phase()`

. Straightforward and direct. Requires importing`cmath`

library. It’s specific to complex numbers.**Method 2:**Using`math.atan2()`

. Provides more control by manually inputting the real and imaginary parts. Uses standard math library. Good for educational purposes.**Method 3:**Using`numpy.angle()`

. Ideal for numerical computations with arrays. Requires NumPy library. Best for large-scale operations with complex numbers.**Method 4:**Using`cmath.polar()`

. Returns extra information that could be useful in some contexts. Covers broader functionality for complex numbers.**Method 5:**Lambda Function. Compact and reusable. Good for inline usage. Masks the underlying function, which could be a downside if clarity is required.