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 $\theta = \pi$:

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

$\blacksquare$

Source of Name

This entry was named for Leonhard Paul Euler.