ComplexExpand

ComplexExpand[expr] expands expr assuming that all variables are real.

ComplexExpand[expr, , , ... ] expands expr assuming that variables matching any of the are complex.

Example: ComplexExpand[Sin[x + I y]] .

The variables given in the second argument of ComplexExpand can be patterns.

Example: ComplexExpand[Sin[x], x] .

The option TargetFunctions can be given as a list of functions from the set {Re, Im, Abs, Arg, Conjugate, Sign}. ComplexExpand will try to give results in terms of functions specified.

ComplexExpand[expr, vars, TargetFunctions -> Abs, Arg] converts to polar coordinates.

See Section 1.4.5 and Section 3.3.8.

See also: GaussianIntegers, TrigToExp, ExpToTrig, TrigExpand, FunctionExpand.

New in Version 2.

Further Examples