Hyperbolic Tangent in terms of Tangent

Theorem
Let $z \in \C$ be a complex number.

Then:


 * $i \tanh z = \map \tan {i z}$

where:
 * $\tan$ denotes the tangent function
 * $\tanh$ denotes the hyperbolic tangent
 * $i$ is the imaginary unit: $i^2 = -1$.

Also see

 * Hyperbolic Sine in terms of Sine
 * Hyperbolic Cosine in terms of Cosine
 * Hyperbolic Cotangent in terms of Cotangent
 * Hyperbolic Secant in terms of Secant
 * Hyperbolic Cosecant in terms of Cosecant