## Expanding (8 + 3i)<sup>2</sup>

This article will walk through the process of expanding and simplifying the expression (8 + 3i)<sup>2</sup>, where 'i' represents the imaginary unit (√-1).

### Understanding the Basics

**Imaginary Unit:**The imaginary unit 'i' is defined as the square root of -1. This allows us to work with the square roots of negative numbers.**Complex Numbers:**A complex number is a number of the form*a + bi*, where*a*and*b*are real numbers and 'i' is the imaginary unit.

### Expanding the Expression

To expand (8 + 3i)<sup>2</sup>, we use the FOIL method:

**F**irst: 8 * 8 = 64**O**uter: 8 * 3i = 24i**I**nner: 3i * 8 = 24i**L**ast: 3i * 3i = 9i<sup>2</sup>

Combining the terms: 64 + 24i + 24i + 9i<sup>2</sup>

### Simplifying the Expression

Remember that i<sup>2</sup> = -1. Substituting this into our expression:

64 + 24i + 24i + 9(-1)

Simplifying further:

64 + 48i - 9

### Final Result

Combining real and imaginary terms:

**(8 + 3i)<sup>2</sup> = 55 + 48i**

Therefore, the simplified form of (8 + 3i)<sup>2</sup> is **55 + 48i**.