Check out this mathworld site: http://mathworld.wolfram.com/i.html
Basically you start out with the Euler formula . When you test the value , you simply get i, so now we can say that . So, . And simple power rules show from here that it reduces to
It makes sense after I go through all of the steps, but I agree I don't see a logical explanation of why this works the way it does. The mysteries of math.