Question

Which answer is equal to i³⁹?
A. 1
B. -i
C. i
D. -1

Answer 1

To find i³⁹, divide the exponent by 4 to find the remainder. The remainder corresponds to the position in the cycle of powers of i. In this case, i³⁹ is equal to -i.

Step-by-step explanation:

To find i³⁹, we need to determine the pattern of the powers of i. The powers of i cycle in a pattern: i, -1, -i, and 1. Since i⁴ = 1, we can divide the exponent 39 by 4 to find the remainder. 39 divided by 4 is 9 with a remainder of 3. Therefore, i³⁹ is equal to i³, which is -i. So the answer is B. -i.