## Expanding (8 – 5i)<sup>2</sup>

This article will guide you through the process of expanding the expression (8 – 5i)<sup>2</sup>.

### Understanding Complex Numbers

Before we dive into the expansion, let's recap what complex numbers are. A complex number is a number of the form **a + bi**, where:

**a**and**b**are real numbers.**i**is the imaginary unit, defined as the square root of -1 (i<sup>2</sup> = -1).

### Expanding the Expression

We can expand (8 – 5i)<sup>2</sup> using the following steps:

**Apply the square:**(8 – 5i)<sup>2</sup> = (8 – 5i)(8 – 5i)**Use the distributive property (FOIL method):****F**irst: 8 * 8 = 64**O**uter: 8 * (-5i) = -40i**I**nner: (-5i) * 8 = -40i**L**ast: (-5i) * (-5i) = 25i<sup>2</sup>

**Combine like terms:**64 - 40i - 40i + 25i<sup>2</sup> = 64 - 80i + 25i<sup>2</sup>**Substitute i<sup>2</sup> with -1:**64 - 80i + 25(-1) = 64 - 80i - 25**Simplify:**39 - 80i

### Final Result

Therefore, (8 – 5i)<sup>2</sup> expands to **39 - 80i**.