Hyperbolic Cosine in terms of Cosine

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

Then:


 * $\cosh z = \map \cos {i z}$

where:
 * $\cos$ denotes the complex cosine
 * $\cosh$ denotes the hyperbolic cosine
 * $i$ is the imaginary unit: $i^2 = -1$.

Also see

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