The thing about that is that an imaginary power of a number isn't really simple - it's not like you can do repeated multiplication "i*pi times" and get a result

The thing about that is that an imaginary power of a number isn't really simple - it's not like you can do repeated multiplication "i*pi times" and get a result. An imaginary power is defined as cosx + isinx (or the equivalent Taylor series). That's what I meant when I said that all people are impressed by is that cos(pi) = -1 or that sin(pi) = 0.