Simplify the expressions.

i^23

-i

Step-by-step explanation:

i^0=1

i^1=i

i^2=-1

i^3=-i

i^4=1

This repeats so we want to see how many 4 factors of i there is in i^ (23) which is 5 with a remainder of 3.

So i^ (23) = i^3=-i.

i^ (23) = i^ (5*4+3) = (i^4) ^5 * (i^3) = (1) ^5 * (-i) = 1 (-i) = -i.