How do you manually calculate i to the power of i?

Answer 1

i (taken to be sqrt(-1) for this question) requires that you know a bit about writing complex numbers.

i = e^(i*pi/2)

so i^i = (e^(i*pi/2))^i

which equals e^(i*i*pi/2)

since i*i = -1 we get e^(-pi/2)

so i^i = e^(-pi/2)

which is roughly .207879576