Euler's Identity

Theorem

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

Proof
Follows directly from Euler's Formula $$e^{i \theta} = \cos \theta + i \sin \theta$$, by plugging in $$\theta = \pi$$:


 * $$e^{i \pi} + 1 = \cos \pi + i \sin \pi + 1 = -1 + i \times 0 + 1 = 0$$