1/i^20 + 1/i^21 I got 1-i but i am not sure if that is right.
Correct. You know that i^2 = -1, therefore i^4 = 1. And from this it follows that if n is a multiple of 4 you have i^n = 1. So, i^(-20) = 1 and
i^(-21) = 1/i = -i. The fact that
1/i = -1 can be seen as follows:
i^2 = -1 ---> (divide both sides by i)
i = -1/i --->
1/i = -i.