Tangent of Complex Number/Formulation 2

Theorem
Let $a$ and $b$ be real numbers.

Let $i$ be the imaginary unit.

Then:
 * $\tan \left({a + b i}\right) = \dfrac {\tan a + i \tanh b} {1 - i \tan a \tanh b}$

where:
 * $\tan$ denotes the tangent function (real and complex)
 * $\tanh$ denotes the hyperbolic tangent function.

Also see

 * Sine of Complex Number
 * Cosine of Complex Number
 * Cosecant of Complex Number
 * Secant of Complex Number
 * Cotangent of Complex Number