Re: Abs and variables

• To: mathgroup at smc.vnet.net
• Subject: [mg4335] Re: Abs and variables
• From: espen.haslund at fys.uio.no (Espen Haslund)
• Date: Thu, 11 Jul 1996 00:58:15 -0400
• Organization: Universitet i Oslo
• Sender: owner-wri-mathgroup at wolfram.com

```>
>        How can I have the Abs function treat real variables properly?
>I seem to recall a way of declaring a variable real, but I don't
>remember how.  If there is such a way, would this work with Abs; i.e.
>fix the variable a so that "Abs[a]" will give a result of "a"?
>
>Thanks.
>
>/
>:@-) Scott
>\

Hi, Scott
I think you can obtain what want by using ComplexExpand with
the Option TargetFunctions->{Re, Im}. The optional
second argument of ComplexExpand specifies parameters to be
Complex (the rest is assumed to be real).

Below are two examples that I hope may be of some help.
(I think the manual is too brief on ComplexExpand)

-Espen

IN:  z = 1 / (1/r1 + I w c) + r2

1
OUT: r2 + ----------
1
-- + I c w
r1

IN:  ComplexExpand[Abs[z],
TargetFunctions->{Re, Im} ] //Simplify

2               2    2   2   2  2
r1  + 2 r1 r2 + r2  + c  r1  r2  w
OUT: Sqrt[-----------------------------------]
2   2  2
1 + c  r1  w

IN:  z = 1 / (1/r1 + I w c) + z2

1
OUT: ---------- + z2
1
-- + I c w
r1

IN: ComplexExpand[Abs[z], {z2},
TargetFunctions->{Re, Im} ] //Simplify

c w                2
OUT: Sqrt[(-(------------) + Im[z2])  +
-2    2  2
r1   + c  w

1                2
(------------- + Re[z2]) ]
1     2     2
-- + c  r1 w
r1

==== [MESSAGE SEPARATOR] ====

```

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