Cosine in terms of Hyperbolic Cosine

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

Then:


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

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

Also see

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