What is the most intuitive explanation for euler's identity? [duplicate]

Is there any intuitive explanation for: $$e^{i\pi} + 1 = 0$$

About whether this question is a duplicate, what is asked for is not a proof but an explanation that helps with the not-so-intuitive aspects of the identity.

marked as duplicate by Zev Chonoles, Andrew D. Hwang, Claude Leibovici, Jonas Meyer, drhabJun 18 '15 at 16:07

• $-1$ is one unit to the left ($\pi$ radians from the right, i.e. postive direction) of $0$? – martini Jun 18 '15 at 12:35
• If you think of $e^{i \theta}$ as a clockwise rotation of angle $\theta$ radians or remember $e^{i \theta} = \cos \theta + i \sin \theta$, then $e^{i \pi}$ is fairly obviously $-1$ – Henry Jun 18 '15 at 12:40