I like the solution to x = e^x, the fixed point of f(x)=e^x.
It's the complex number you get by taking the natural log of any number (other than 1 or 0) an infinite amount of times.
What is presented in that article is the best description I've seen for what it actually means for a number to be the square root of -1. But maybe I've just lived a sheltered mathematical life.
Anyway, the answer to the riddle i2 = -1 is i = (1, 90o)