Here's an easy way to simplify higher powers of i.

First know the first 3 powers of i

i^1 = sqrt(-1)
i^2 = -1
i^3 = -i


To get any power of i greater than 4, simply divide by 4 and the integer value remainder gives the answer. It will be one of the above.

Example:

i^45....   45 divided by 4 is 11 with a remainder of 1, so the answer is sqrt(-1)

i^202..... 202 divided by 4 is 50 with a remainder of 2, so the answer is -1

i^79.... 79 divide by 4 is 19 with a remainder of 3, so the answer is -i