Sine of Complex Number

Theorem
Let $a$ and $b$ be real numbers.

Let $i$ be the imaginary unit.

Then:
 * $\sin \paren {a + b i} = \sin a \cosh b + i \cos a \sinh b$

where:
 * $\sin$ denotes the sine function (real and complex)
 * $\cos$ denotes the real cosine function
 * $\sinh$ denotes the hyperbolic sine function
 * $\cosh$ denotes the hyperbolic cosine function.

Also see

 * Cosine of Complex Number
 * Tangent of Complex Number
 * Cosecant of Complex Number
 * Secant of Complex Number
 * Cotangent of Complex Number