Mathematica 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.
I () — , entered as EsciiEsc ("imaginary i")
FullSimplify — simplify hyperbolic function expressions
FunctionExpand — reduce to algebraic forms or simpler arguments
ComplexExpand — expand into real and imaginary parts