ComplexExpand

ComplexExpand[expr]

expands expr assuming that all variables are real.

ComplexExpand[expr,{x1,x2,}]

expands expr assuming that variables matching any of the xi are complex.

Details and Options

Examples

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Basic Examples  (2)

Assume both x and y are real:

Take x to be complex:

Scope  (5)

Polynomials:

Trigonometric and hyperbolic functions:

Inverse trigonometric and inverse hyperbolic functions:

Exponential and logarithmic functions:

Composition of functions:

Options  (1)

TargetFunctions  (1)

This gives an answer in terms of Re[z] and Im[z]:

With TargetFunctions->{Abs, Arg}, the answer is given in terms of Abs[z] and Arg[z]:

Use Conjugate as the target function:

Properties & Relations  (1)

This computes Re[Sin[x+I y]] assuming that x and y are real:

The same computation can be done using TrigExpand and Refine:

Introduced in 1991
 (2.0)
 |
Updated in 2007
 (6.0)