## Euler's identity

A remarkable identity in mathematics is the following: $e^{i\pi} + 1 = 0.$ This identity relates five fundamental mathematical constants and is called “the most beautiful math formula” by some.

A proper proof of this identity involves complex analysis and is beyond the scope of these notes. The key to proving the identity is the following more general result: $e^{ix} = \cos x + i\sin x.$ Then, setting $$x = \pi$$ gives us Euler's identity.

Watch Salman Khan's video below for an informal sketch of the proof that $$e^{ix} = \cos x + i\sin x.$$