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 [MEDIA=youtube]0qeXs5eWcqU[/MEDIA]