Definition:Inverse Hyperbolic Cosine/Complex/Definition 2

Definition
The inverse hyperbolic cosine is a multifunction $\cosh^{-1}: \C \to \C$ defined as:


 * $\forall x \in \C: \cosh^{-1} \left({x}\right) = \ln \left({x + \sqrt{x^2 - 1} }\right)$

where $\ln$ is the complex natural logarithm function.

As $\ln$ is a multifunction it follows that $\cosh^{-1}$ is likewise a multifunction.

Also see

 * Equivalence of Definitions of Inverse Hyperbolic Cosine


 * Definition:Inverse Hyperbolic Sine
 * Definition:Inverse Hyperbolic Tangent
 * Definition:Inverse Hyperbolic Cotangent
 * Definition:Inverse Hyperbolic Secant
 * Definition:Inverse Hyperbolic Cosecant