Simplify each of the following powers of i. i^99=

I= sqrt (-1)

If the power is
- even then the value could be -1 or 1
-odd then the value could be -i or i

99 is odd so now is
-i if (99+1)/2 is even or is
i is (99+1)/2 is odd

Now check (99+1)/2= 100/2= 50,
50 is even so
i^99 = -i