**π‘ Problem Formulation:** Working with complex numbers in Python necessitates understanding operations such as squaring, which is a fundamental mathematical operation. We aim to take a complex number as input, say `3 + 4j`

, and return its square, in this case, `-7 + 24j`

.

## Method 1: Using the Python Complex Number Type

Python has built-in support for complex numbers, and squaring a complex value can be as straightforward as using the usual multiplication operator. The `**`

operator can raise any number, including a complex number, to the power of 2.

Here’s an example:

z = 3 + 4j result = z ** 2 print(result)

Output: `(-7+24j)`

This code snippet creates a complex number using Python’s literal notation and then squares it using the exponentiation operator. The output is the square of the complex number as another complex number.

## Method 2: Using the Complex Number’s Attributes

Complex numbers in Python have two attributes, `.real`

and `.imag`

, that hold the real and imaginary parts, respectively. To manually square a complex number, you can apply the algebraic rule (a+bi)(a+bi) = a^2 + 2abi – b^2.

Here’s an example:

z = 3 + 4j result = (z.real ** 2 - z.imag ** 2) + (2 * z.real * z.imag) * 1j print(result)

Output: `(-7+24j)`

By manually performing the multiplication of the complex number by itself, this code snippet provides the square through understanding of the nature of complex numbers.

## Method 3: Using the `cmath`

Module

The `cmath`

module provides mathematical functions for complex numbers. The `cmath`

module can handle operations for squaring complex values with built-in functions, maintaining precision and handling edge cases properly.

Here’s an example:

import cmath z = 3 + 4j result = cmath.pow(z, 2) print(result)

Output: `(-7+24j)`

This code uses the `cmath.pow()`

function to raise the complex number to the power of 2. The `cmath`

module is specifically designed to deal with complex numbers, making it robust for this type of operation.

## Method 4: Using `numpy`

for Complex Array Operations

If you’re working with arrays of complex numbers, the `numpy`

library offers vectorized operations that are efficient and convenient. The numpy array multiplication can square each element in an array of complex numbers in one go.

Here’s an example:

import numpy as np z = np.array([3 + 4j]) result = z ** 2 print(result)

Output: `[-7.+24.j]`

This code snippet demonstrates squaring a complex number using `numpy`

‘s powerful array operations, which is highly useful when dealing with multiple complex numbers at once.

## Bonus One-Liner Method 5: Using Lambda Functions

For quick, inline operations, a lambda function can be used to square a complex number. This is not the most readable or conventional method, but it showcases the flexibility of Python.

Here’s an example:

square = lambda z: z**2 result = square(3 + 4j) print(result)

Output: `(-7+24j)`

This one-liner uses a lambda function to define an operation that squares a complex number. It then applies this to our example and prints the result.

## Summary/Discussion

**Method 1:**Direct use of Python’s complex type. Strengths: Straightforward, no imports required. Weaknesses: Lacks the explicitness of algebraic operation.**Method 2:**Applying algebraic rules manually. Strengths: Educational, makes the operation clear. Weaknesses: Verbose, can be prone to human error.**Method 3:**Using`cmath`

module. Strengths: Performs precise complex number arithmetic. Weaknesses: Requires an additional import.**Method 4:**Utilizing`numpy`

. Strengths: Suitable for array operations, highly efficient. Weaknesses: Overkill for single numbers, requires numpy installation.**Method 5:**Lambda one-liner. Strengths: Compact, good for inline operations. Weaknesses: Could be considered less readable, not conventional for 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.