Hyperbolic Functions

The Wolfram Language supports hyperbolic functions everywhere in the complex plane—with careful attention to branch cuts—and provides an extensive web of exact and algebraic transformations, together with efficient arbitrary-precision numerical evaluation.

(RefLink[I, paclet:ref/I]) ((RefLink[i, paclet:ref/I])) — (Sqrt[-1]), entered as (Key0[esc]) ii (Key0[esc]) ("imaginary i")

(RefLink[FullSimplify, paclet:ref/FullSimplify]) — simplify hyperbolic function expressions

(RefLink[FunctionExpand, paclet:ref/FunctionExpand]) — reduce to algebraic forms or simpler arguments

(RefLink[TrigToExp, paclet:ref/TrigToExp]), (RefLink[ExpToTrig, paclet:ref/ExpToTrig]) — convert between hyperbolic and exponential functions

(RefLink[ComplexExpand, paclet:ref/ComplexExpand]) — expand into real and imaginary parts