Definition:Inverse Hyperbolic Sine/Real/Definition 2

Definition
The principal branch of the real inverse hyperbolic sine function is defined as:
 * $\operatorname{arcsinh} \left({z}\right) = \dfrac 1 i \ln \left({i z + \sqrt{1 - z^2} }\right)$

Also see

 * Derivation of Real Arcsine from Inverse Hyperbolic Sine Multifunction