Final answer:
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:
- i^1 = i
- i^2 = i · i = -1 (since i is the square root of negative one)
- i^3 = i^2 · i = (-1) · i = -i
Therefore, the value of i^3 is -i.