i^i means WHAT?!?!?!?!?! My friend gave me the brain-teaser "i^i = what?", and with a little bit of coaching I finally discovered that i^i = e^(-pi/2) Which is cool, I suppose. But the more I think about it, the more I wonder: what the heck does it mean??? For that matter, what does anything raised to an imaginary power mean? For instance: e^(ix) = cos(x)+i*sin(x) It's so counter-intuitive, is there some way to make sense of it by analogy with real numbers? Or will it just remain abstract until the end of time?