Tangent Exponential Formulation

Theorem
For any complex number $x$,
 * $ \displaystyle \tan x = i \frac { 1 - e^{2ix} }{ 1 + e^{2ix} } $

where $\tan x$ is the tangent and $i^2 = -1$.

Also see

 * Sine Exponential Formulation
 * Cosine Exponential Formulation
 * Arctangent Logarithmic Formulation