## Expanding and Simplifying (8 + 3i)^2

This article will guide you through the process of expanding and simplifying the expression (8 + 3i)².

### Understanding Complex Numbers

Before we begin, let's quickly review complex numbers. A complex number is a number that can be expressed in the form *a + bi*, where *a* and *b* are real numbers, and *i* is the imaginary unit, defined as the square root of -1.

### Expanding the Expression

To expand (8 + 3i)², we can use the FOIL (First, Outer, Inner, Last) method or simply distribute:

(8 + 3i)² = (8 + 3i)(8 + 3i)

**Using FOIL:**

**First:**8 * 8 = 64**Outer:**8 * 3i = 24i**Inner:**3i * 8 = 24i**Last:**3i * 3i = 9i²

**Combining the terms:**

64 + 24i + 24i + 9i²

### Simplifying the Expression

Remember that i² = -1. Substitute this into our expression:

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

Simplify further:

64 + 48i - 9

**Final Result:**

**(8 + 3i)² = 55 + 48i**

Therefore, the simplified form of (8 + 3i)² is 55 + 48i.