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

-i is the answer