Question

Simplify each of the following powers of i.
a) i
b) i²
c) i³
d) i⁴

Answer 1

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