Question

Simplify each of the following powers of i into either −1, 1, i, or -i .
a i²

Answer 1

The expression i² simplifies to -1, as the imaginary unit i is defined as the square root of -1.

Step-by-step explanation:

To simplify the expression i2, we need to remember that i is the imaginary unit, which is defined as the square root of -1. This means that i2 is equivalent to (√-1)2, which simplifies to -1.

Therefore, i2 = -1. This is one of the fundamental properties of the imaginary unit and is used extensively when working with complex numbers.