complex numbers

If the power is divisible by 2 and not 4, it is -1.

If the power is divisible by 4, it is 1.

If it satisfys none of those conditions, it is i or -i.

(basically, it is a pattern of i, -1, -i, and 1)

So, let's see what i^11 is. By running down the list, it satisfys only -i. Which means, i^11 is -i.

i^16 is divisible by 4, so it is 1.

Keep on going like this until you have the answer!

:)

we know that i^2=-1 so we can have the equation -i+1+i+-1+-i which simplifies to  -i+1+i-1-i where i and -1 cancel and the 1 and -1 cancel to get -i

so this equation simplifies to -i

\(-i\)