What is the value of i^3?

To find the value of i^3, we start by recalling that i represents the imaginary unit, defined as the square root of -1. From this definition, we can establish some important powers of i:

1. i^1 = i

2. i^2 = -1

3. i^3 = i^2 * i = (-1) * i = -i

4. i^4 = (i^2)^2 = (-1)^2 = 1

With these calculations, we can see that i^3 equals -i. Therefore, this is why the correct answer is -i.

Recognizing these relationships simplifies understanding higher powers of i, as the cycle of values (i, -1, -i, 1) continues to repeat every four powers. This cyclical nature of the powers of i is crucial for handling complex numbers and related calculations in mathematics.