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 \(e^{ix} = \cos x + i\sin x.\)