Euler's Identity

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

Proof
Falls directly from Euler's formula ($$e^{i\theta}=\cos\theta + i\sin\theta$$), by plugging in $$\theta=\pi$$.

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