A root of unity is a complex number that yields 1 when raised to some nth root.

i is defined to be (-1)^(1/2)

i^2 then would be (-1)^(1/2)^2 = (-1)^(2/2) = (-1)^1 = -1

i^3 would be i^2 * i = -1 *i = -1

i^4 would be i^2 * i^2 = -1 * -1 = 1

Every fourth term will result in a value of 1.