Modulus of Sine of Complex Number

Theorem
Let $z = x + i y \in \C$ be a complex number, where $x, y \in \R$.

Let $\sin z$ denote the complex sine function.

Then:
 * $\cmod {\sin z} = \sqrt {\sin^2 x + \sinh^2 y}$

where:
 * $\cmod z$ denotes the modulus of a complex number $z$
 * $\sin x$ denotes the real sine function
 * $\sinh$ denotes the hyperbolic sine function.