What is the value of the imaginary unit i when raised to the power of 5 (i⁵)?

To find the value of the imaginary unit i raised to the power of 5, it is helpful to understand the powers of i. The imaginary unit i is defined as the square root of -1, and it follows a cyclical pattern when raised to successive powers:

• i¹ = i
• i² = -1

• i³ = -i
• i⁴ = 1

After reaching i⁴, the pattern repeats itself. This means that powers of i can be reduced by modulo 4.

Now, to find i⁵, we can observe that 5 divided by 4 leaves a remainder of 1. Thus, i⁵ can be expressed as i raised to the power of the remainder when divided by 4:

i⁵ = i^(4+1) = i⁴ * i¹ = 1 * i = i.

Therefore, the value of i raised to the power of 5 is i, confirming that the correct answer is indeed C.