Sine Exponential Formulation/Proof 2

Theorem
For any complex number $x$,


 * $ \displaystyle \sin x = \frac 1 2 i \left({ e^{-i x} - e^{i x} }\right)$

where $\sin x$ is the sine and $i^2 = -1$.

Proof
Recall Euler's Formula:


 * $ \displaystyle e^{ix} = \cos x + i \sin x $

Then, starting from the RHS: