math
posted by alicia on .
How do you evaluate i to large powers such as i^1992, i^1993, and i^2000 without a calculator?

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