Question

How do you evaluate i to large powers such as i^1992, i^1993, and i^2000 without a calculator?

Answer 1

since i^2 = -1, i^4 = 1.

So, divide the power by 4, since every factor of i^4 is just 1.

You will be left with one of the following:

i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i

For example, i^913 = i^1 = i