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Re: How to get the Real and Imaginary part of an expression

• To: mathgroup at smc.vnet.net
• Subject: [mg129328] Re: How to get the Real and Imaginary part of an expression
• From: "Nasser M. Abbasi" <nma at 12000.org>
• Date: Sat, 5 Jan 2013 02:17:05 -0500 (EST)
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• Reply-to: nma at 12000.org

On 1/2/2013 8:14 PM, Eduardo M. A. M. Mendes wrote:
> Hello
>
> I need to extract the real and imaginary part of the following expression
>
> (w=882)/(s^2+2*z*w*s+w^2)
>
> where w and z are positive constants.  s is a complex variable.
>
> Applying Re and Im to the expression does not do much.   By hand, one can easily find them.
>

You can use ComplexExpand.

For example

----------------
expr = s + 2 I b + c
ComplexExpand[Re[expr]]
   (* c + s *)

ComplexExpand[Im[expr]]
   (* 2 b *)
-------------------

For your example, I might do

Clear[s, z, w, a, b];
expr = w/(s^2 + 2*z*w*s + w^2);
ComplexExpand[Re[expr /. s -> a + I b]]

--Nasser