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MathGroup Archive 2006

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Re: Simplification and Arg[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66604] Re: Simplification and Arg[]
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Mon, 22 May 2006 18:14:40 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <e4r7qm$mmh$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <e4r7qm$mmh$1 at smc.vnet.net>,
 Andrew Moylan <andrew.moylan at anu.edu.au> wrote:

> Should Mathematica be able to simplify the following expression? (It is 
> easily seen to be zero under the given condition, x > 0.)
> 
> FullSimplify[
> 	Arg[1 + I * x] + Arg[1 - I * x],
> 	{x > 0}
> ]
> 
> In particular, I would have expected the following to yield ArcTan[b / 
> a], from which the above expression is easily reduced to zero:
> 
> FullSimplify[
> 	Arg[a + I b],
> 	{a > 0, b > 0}
> ]
> 
> Any ideas?

I would use ComplexExpand instead of FullSimplify:

  ComplexExpand[Arg[I*x + 1] + Arg[1 - I*x], TargetFunctions -> {Re, Im}]

  0

  ComplexExpand[Arg[a + I b], TargetFunctions -> {Re, Im}]
  ArcTan[a, b]

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    
AUSTRALIA                               http://physics.uwa.edu.au/~paul


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