$$e^{\pi i} + 1 = 0$$

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?

$$e^{i\pi}=\lim\limits_{N\to\infty}\left(1 + \frac{iπ}{N}\right)^N$$


