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Re: Real and Imaginary Parts of complex functions

• To: mathgroup at smc.vnet.net
• Subject: [mg129945] Re: Real and Imaginary Parts of complex functions
• From: Szabolcs HorvÃt <szhorvat at gmail.com>
• Date: Wed, 27 Feb 2013 03:08:18 -0500 (EST)
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On 2013-02-26 06:09:00 +0000, Brentt said:

> 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?

You can use ComplexExpand for this.

In[8]:= ComplexExpand[Re[1/(x + y I)]]
Out[8]= x/(x^2 + y^2)

See also http://mathematica.stackexchange.com/q/9340/12 and the links within.