How do you simplify # i^5#?
This is the same as i
The complex i repeats after 4 powers
This can be seen with
i^1 = i
i^3 = i^2 * i = -1 * i => -i
i^4 = i^2 * i^2 => -1 * -1 >>> 1
After this, we can take the mod 4 of the exponent
(in this case we can just do the next exponent, try it out and of course the answer will be the same as i ^ 1 )
Thus, the answer is i.