Question

Simplify the expressions.
i^23

Answer 1

-i

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.