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

Also see

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