e^(pi)i + 1 = 0

I have been searching for a convincing interpretation of this. I understand how it comes about but what is it that it is telling us? 

Best that I can figure out is that it just emphasizes that the various definitions mathematicians have provided for non-intuitive operations (complex exponentiation, concept of radians etc.) have been particularly inspired. Is that all that is behind the slickness of the Famous Five equation?

Any pointers?