Definition:Inverse Hyperbolic Cosine/Complex/Principal Branch

Definition
The principal branch of the complex inverse hyperbolic cosine function is defined as:
 * $\forall z \in \C: \operatorname {Cosh}^{-1} \paren z := \Ln \paren {z + \sqrt {z^2 - 1} }$

where:
 * $\Ln$ denotes the principal branch of the complex natural logarithm
 * $\sqrt {z^2 - 1}$ denotes the principal square root of $z^2 - 1$.

Also see

 * Derivation of Hyperbolic Arccosine from Inverse Hyperbolic Cosine Multifunction