## Understanding (8i)^2

This expression involves the imaginary unit **i**, which is defined as the square root of -1 (√-1). Let's break down how to simplify (8i)^2:

### Applying the Exponent

Remember that squaring a term means multiplying it by itself:

(8i)^2 = (8i) * (8i)

### Multiplication of Complex Numbers

To multiply complex numbers, we distribute as we would with regular binomials:

(8i) * (8i) = 8 * 8 * i * i = 64 * i^2

### The Key: i^2 = -1

Since **i** is the square root of -1, squaring it results in -1:

i^2 = (√-1)^2 = -1

### Final Simplification

Substituting i^2 with -1 in our expression:

64 * i^2 = 64 * (-1) = -64

## Therefore, (8i)^2 = -64.

This demonstrates that squaring an imaginary number results in a real number.