Sine in terms of Hyperbolic Sine

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

Then:


 * $i \sin z = \sinh \paren {i z}$

where:
 * $\sin$ denotes the complex sine
 * $\sinh$ denotes the hyperbolic sine
 * $i$ is the imaginary unit: $i^2 = -1$.

Also see

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