Raising the powers of i, a pattern develops.

i^1 = i

i^2 = -1

i^3= -i

i^4= 1

i^5= i

Raising the powers of -i, another pattern develops.

(-i)^1 = -i

(-i)^2 =-1

(-i)^3 = i

(-i)^4 = 1

(-i)^5 = -i

So when the powers of i and -i is multiples of 4, their exponents are both equal to 1. That is,

When n=24 , i^n+(-i)^n=1=1=2