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Topic: Real and Imaginary Parts of complex functions
Replies: 3   Last Post: Feb 27, 2013 3:04 AM

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Murray Eisenberg

Posts: 2,105
Registered: 12/6/04
Re: Real and Imaginary Parts of complex functions
Posted: Feb 27, 2013 3:04 AM
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Did you try a search in the Documentation Center? If you do, one of the things you'll find near the top of the hits is

Complex Numbers (Mathematica Guide)

which includes a list of functions. One of these is:

ComplexExpand - expand symbolic expressions into real and imaginary parts

Then look at the reference page for that; it's what you want here.

ComplexExpand[Re[1/(x + y I)]]
x/(x^2 + y^2)

The Refine and the assumptions about x and y are superfluous: the whole point of ComplexExpand is that it assumes symbolic variables used within it are already real.

On Feb 26, 2013, at 1:09 AM, Brentt <> wrote:

> Hello,
> I was wondering why this works
> IN[]:= Refine[Re[x + y I], Element[x , Reals] && Element[y , Reals]]
> Out[]:= x
> But this does not
> In[]:= Refine[Re[1/(x + y I)], Element[x , Reals] && Element[y , Reals]]
> Out[]:= Re[1/(x + y I)]
> Is there a nice built in way to get the real and imaginary parts of a
> complex function?

Murray Eisenberg
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2838 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305

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