Question

What is the simplified form of i^15?
O A. -1
O B. 1
O C. -i
O D. i

Answer 1

To simplify i^15, we divide the exponent by 4 and find the remainder, which tells us the position in the pattern of powers of i. Since the remainder is 3, i^15 simplifies to -i.

Step-by-step explanation:

The question asks for the simplified form of i^15. To find this, we should remember that the powers of i (the imaginary unit) follow a pattern: i, -1, -i, 1, and then the pattern repeats every fourth power. Therefore, to simplify i^15, we can divide the exponent by 4 and find the remainder to determine where we are in the pattern.

In this case, 15 divided by 4 leaves a remainder of 3. This corresponds to the third number in our pattern, which is -i. So, i^15 simplifies to -i, which means the correct answer is Option C.