Find i^100

[math_celebrity]

i = sqrt(-1)
i^2 = sqrt(-1)*sqrt(-1) = -1
i^3 = I^2 * I = -sqrt(-1)
i^4 = I^2 * I^2 = -1 * -1 = 1

i^100 can be broken down. The easiest way is to check for powers of 4:
100 = 25 * 4 so we have:
(i^4)^25
i^4 = 1, so we have:
(i)^25 = 1