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

• To: mathgroup at smc.vnet.net
• Subject: [mg129327] Re: How to get the Real and Imaginary part of an expression
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 5 Jan 2013 02:16:45 -0500 (EST)
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• References: <20130103021627.CBD1368B0@smc.vnet.net>

expr = (w = 882)/(s^2 + 2*z*w*s + w^2);

re = Re[ComplexExpand[expr, s]] //
   Simplify[#, Element[z, Reals]] &;

im = Im[ComplexExpand[expr, s]] //
   Simplify[#, Element[z, Reals]] &;

expr == re + I*im // FullSimplify

True

Using a concrete example

s2 = RandomComplex[] // Rationalize[#, 0] &;

re2 = re /. s -> s2 //
   Simplify[#, Element[z, Reals]] &;

im2 = im /. s -> s2 //
   Simplify[#, Element[z, Reals]] &;


(expr /. s -> s2) == re2 + I*im2 // Simplify

True


Bob Hanlon


On Wed, Jan 2, 2013 at 9:16 PM, Eduardo M. A. M. Mendes
<emammendes at gmail.com> 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.
>
> What am I missing?
>
> many thanks
>
> Ed
>
>
>

• References:
  • How to get the Real and Imaginary part of an expression
    • From: "Eduardo M. A. M. Mendes" <emammendes@gmail.com>