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Re: Simplify this complex expression?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30893] Re: Simplify this complex expression?
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Sun, 23 Sep 2001 02:16:33 -0400 (EDT)
  • References: <9oet9v$ilh$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Aram,

expr=
    Sqrt[-(lam/Im[(d1*lam - f*lam + I*Pi*w0^2)/(d1*d2*lam - d2*f*lam -
    f^2*lam + I*d2*Pi*w0^2)])]/Sqrt[Pi];


ComplexExpand//@expr

    (Sqrt[1/f^2]*Sqrt[1/w0^2]*Abs[d1*d2*lam - d2*f*lam -
         f^2*lam + I*d2*Pi*w0^2])/Pi

Simplify[%,And[d1>0,d2>0,f>0,lam>0,w0>0]]

    Abs[d1*d2*lam - d2*f*lam - f^2*lam + I*d2*Pi*w0^2]/
      (f*Pi*w0)

ComplexExpand[%, TargetFunctions-> {Re,Im}]

    Sqrt[(d1*d2*lam - d2*f*lam - f^2*lam)^2 + d2^2*Pi^2*w0^4]/
          (f*Pi*w0)

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Aram Schiffman" <awacs7 at home.com> wrote in message
news:9oet9v$ilh$1 at smc.vnet.net...
> Hi,
>
> I have this expression:
>
> Sqrt[-(lam/Im[(d1*lam - f*lam + I*Pi*w0^2)/(d1*d2*lam - d2*f*lam -
> f^2*lam +
>        I*d2*Pi*w0^2)])]/Sqrt[Pi]
>
> and I wish to simplify it. (Or other expressions with essentially the
> same structure).  All variables are real and positive, so I want the
> real parts of Im[...] to go away.
>
> It's easy enough by hand, but for various reasons I would like
> Mathematica to do it for me.
>
> I had a general idea to somehow map ComplexSimplify through all levels
> of the expression, and then work my way (somehow) back to the top
> level. Problem is, when I use "Level," the Heads go away; I can't
> automate the reverse process. I can't think of any other approach to
> try.
>
> Is there a way to do this thing?
>
> Thanks in advance,
>
> Aram Schiffman
>




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