Euler's formula is an example of the mathematical
identity e^ix = cos(x)+i*sin(x) for all real values of x. In this case, x=
pi,
cos(pi)=-1 and
sin(x)=0.
Deriving the identity itself involves some knowledge of calculus and combinatorics. You can short-cut it, if you'd like, by looking up Euler's formula in the sci.math FAQ at www.faqs.org.