       Re: Problem with D and Abs

• To: mathgroup at smc.vnet.net
• Subject: [mg60982] Re: [mg60970] Problem with D and Abs
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 6 Oct 2005 04:08:24 -0400 (EDT)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

```Use the second argument to ComplexExpand

D[
ComplexExpand[
Abs[(Conjugate[s11]*gs)/
(1 + Abs[s11]^2*(-1 + gs)) - a0/(1 + ni)] -
Sqrt[ni*(1 - Abs[a0]^2 + ni)]/(1 + ni),
{a0, s11}],
gs] // Simplify

Bob Hanlon

>
> From: Daniele Lupo <danwolf80_no_spam_ at libero.it>
To: mathgroup at smc.vnet.net
> Date: 2005/10/05 Wed AM 02:28:21 EDT
> Subject: [mg60982] [mg60970] Problem with D and Abs
>
> Hi to all.
>
> I've a problem with this expression:
>
> \!\(Abs[\(Conjugate[s11]\ g\_s\)\/\(1 + Abs[s11]\^2\ \((\(-1\) + g\_s)\)\)
> - \
> Ã\_0\/\(1 + N\_i\)] - \@\(N\_i\ \((1 - Abs[Ã\_0]\^2 + N\_i)\)\)\/\(1 +
> N\_i\)\
> \)
>
>
> I want to have derivative in gs. If I use D, I obtain a strange result,
> that invoke Abs'[...], that's not correct, naturally.
>
> I've tried to use PiecewiseExpand, but I've a problem. In this expression,
> \!\(g\_s\) and \!\(N\_i\) are real, while \!\(Ã\_0\) and s11 are complexes.
> I don't know how to create an expansion that consider some symbol as
real,
> and some other as complex.
>
> How can I do it?
>