Tangent of i

Theorem

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

where $\tan$ denotes the complex tangent function and $i$ is the imaginary unit.

Proof 1
We have:

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