If i is raised to an odd power, then it can not simplify to be

A real number

ok so

any even power is i^ (2n) where n is a whole number

if n=1

i^2 = (√-1) ^2=-1

if i^3, then it is equal to (i^2) (i) = (-1) (i) = - i

if i^4, then it is equal to (i^2) (i^2) = (-1) (-1) = 1

therefor

i^1=i

i^2=-1

i^3=-i

i^4=1

then it repeats

look at the odd powers

i and - i

they are complex

therefor

if i is raised to an odd power, it cannot be simplified to be a real number