Cotangent of i

Theorem

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

where $\cot$ denotes the complex cotangent function and $i$ is the imaginary unit.

Proof 1
We have:

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