Hyperbolic Secant in terms of Secant

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

Then:


 * $\sech z = \sec \paren {i z}$

where:
 * $\sec$ denotes the secant function
 * $\sech$ denotes the hyperbolic secant
 * $i$ is the imaginary unit: $i^2 = -1$.

Also see

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