Secant in terms of Hyperbolic Secant

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

Then:


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

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

Also see

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