The first time I tried to understand Euler's formula was about 2 years ago. I didn't need it, I just randomly run across it, when trying to understand a Fourier transformation. The problem was, that I did'nt know what expomentiation to complex number means.

Now I have some free time and I would like to understand it again. So the first question, is it a theorem of some theory, or is it a definition of exponentioation by complex numbers? If it is a theorem, where can I find something about complex exponents?