ComplexExpand[expr] expands expr assuming that all variables are real. ComplexExpand[expr, {x_1, x_2, ...}] expands expr assuming that variables matching any of the x_i are ...

Mathematica usually pays no attention to whether variables like x stand for real or complex numbers. Sometimes, however, you may want to make transformations which are ...

Complicated algebraic expressions can usually be written in many different ways. Mathematica provides a variety of functions for converting expressions from one form to ...

TargetFunctions is an option for functions such as ComplexExpand that specifies what functions to attempt to generate in the output.

Mathematica transparently works with complex variables throughout, not only numerically, but also symbolically—often relying on original results to handle intricate branch ...

Mathematica supports hyperbolic functions everywhere in the complex plane—with careful attention to branch cuts—and provides an extensive web of exact and algebraic ...

Mathematica has fundamental support for both explicit complex numbers and symbolic complex variables. All applicable mathematical functions support arbitrary-precision ...

With careful attention to branch cuts, Mathematica supports trigonometric functions everywhere in the complex plane, with extensive exact and algebraic transformations, ...

Conjugate[z] or z\[Conjugate] gives the complex conjugate of the complex number z.

Mathematica includes functions for performing a variety of specific algebraic transformations. Some are algorithmically straightforward; others include highly sophisticated ...