Cosine of i/Proof 1

Theorem

 * $\displaystyle \cos i = \frac e 2 + \frac 1 {2e}$

where $\cos$ denotes the complex cosine function and $i$ is the imaginary unit.

Proof
We have:

Also:

Therefore:

Then from $\left({1}\right) + \left({2}\right)$: