Re: Real and Imaginary Parts of complex functions

• To: mathgroup at smc.vnet.net
• Subject: [mg129944] Re: Real and Imaginary Parts of complex functions
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Wed, 27 Feb 2013 03:07:58 -0500 (EST)
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• References: <20130226060933.C3A19687D@smc.vnet.net>

```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 <brenttnewman at gmail.com> 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                                    murray at math.umass.edu
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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