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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 the Mathematica book: Section 1.4.5, Section 3.3.8.
See also: GaussianIntegers, TrigToExp, ExpToTrig, TrigExpand, FunctionExpand.
Further Examples
You can expand complex powers.
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You can expand absolute values.
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You can expand complex exponentials, trig functions, and hyperbolic functions.
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You can expand trig and hyperbolic functions of complex arguments.
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Using the TargetFunction option
This is an expansion in terms of z and the absolute value of z.
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Now we expand in terms of polar coordinates.
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Finally, here is an expansion in terms of z and its conjugate.
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THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT. SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION. | | | |
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