Cosine of Complex Number

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

Let $i$ be the imaginary unit.

Then:
 * $\cos \left({a + b i}\right) = \cos a \cosh b - i \sin a \sinh b$

where $\sin$ denotes the complex sine function and $\cos$ denotes the complex cosine function.

Also see

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