**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.