Question

i^23

Answer 1

What is \(i^0\)?

Answer 2

The powers of i cycle through themselves every 4 powers. i^1 = sqrt(-1), i^2 = -1, i^3 = -i, i^4 = 1. Then you start over again, i^5 = sqrt(-1), etc. The way to quickly find out any power of i is to take the power you're given and divide it by 4 and check the remainder. So 23/4 leaves you with a remainder of 3. That means i^23 is the same as i^3, so i^23 = -i.