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ComplexExpand

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

ComplexExpand[expr, {x₁, x₂, ...}]
expands expr assuming that variables matching any of the x_i are complex.

MORE INFORMATION

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

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.

ComplexExpand automatically threads over lists in expr, as well as equations, inequalities and logic functions.

Basic Examples (2)

Assume both x and y are real:

Take x to be complex:

Properties & Relations (1)

GaussianIntegers TrigToExp ExpToTrig TrigExpand FunctionExpand PowerExpand Abs

Putting Expressions into Different Forms

Expressions Involving Complex Variables

Algebraic Transformations

Complex Numbers

Formula Manipulation

Functions of Complex Variables

Hyperbolic Functions

Trigonometric Functions

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