Raising a real number to the power of an imaginary number doesn't make intuitive sense, but it makes some sort of sense to take the Taylor series for e^x and proclaim that it applies to all complex numbers instead of just real ones. Take a look at the Taylor expansions of sin(x), cos(x) and e^x, you'll see that e^(ix) = cos(x) + i sin(x). From there, you'll see why e^(i pi) is -1.