Question

If i= square root of negative one, what is the value of i^3

Answer 1

The value of i^3, where i is the square root of negative one, can be found by using the properties of exponents. i to the power of 3 equals i squared times i, which results in -i.

Step-by-step explanation:

To determine the value of i^3, we first must understand what i represents. In mathematics, i is defined as the square root of negative one. Knowing that, we can compute i raised to any power using the fundamental properties of exponents and the fact that i to the power of 4 is equal to 1, as i^2 is -1 and i^4 is (i^2)^2, which is (-1)^2=1.

Let's calculate i^3:

1. i^1 = i
2. i^2 = i · i = -1 (since i is the square root of negative one)
3. i^3 = i^2 · i = (-1) · i = -i

Therefore, the value of i^3 is -i.