ok, one of the really cool theorums of math (I think it came from Euler) is
e^(i(pi))=-1
I'm not gonna do the whole proof, but it comes from properties of complex numbers, that if complex number Z=r(coso+sino) then Z^n=r^n(cosno+isinno)
by somthing Euler says e^io=cos0+isino, use pi for o and get e^ipi=-1
pretty cool, huh? relates everything important, including 1, e, i, and pi
I just learned it last semester, so hopefully someone else can explain better why that works, I'm only a freshman
btw, take natural logarithm of both sides, you get what you found on your calculator
peace