So e^(0+ipi) is equal to minus 1 because the real part of zero sets it to 1 and then the imaginary exponentiation acts as a rotation of exactly pi radians.
Why do different numbers to be exponentiated (like 2^0+ipi) give different points on the unit circle? Is there a rule that explains for any x to be exponentiated to a purely imaginary exponent exactly how much rotation you'll get without calculating it to see what happens?