Final answer:
To simplify powers of i, we can calculate the powers of i by using its definition as the square root of -1. The powers of i are: i, -1, -i, and 1.
Step-by-step explanation:
An imaginary number is a concept in mathematics that extends the real numbers by introducing the imaginary unit, denoted by i. The imaginary unit is defined as the square root of -1.
To simplify powers of i, we need to recall that i is defined as the square root of -1. So, let's calculate the powers of i:
a) i = i
b) i² = (i)(i) = -1
c) i³ = (i)(i²) = (i)(-1) = -i
d) i⁴ = (i)²² = (-1)² = 1