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MathGroup Archive 2006

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Re: Simplification and Arg[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66596] Re: Simplification and Arg[]
  • From: Peter Pein <petsie at dordos.net>
  • Date: Mon, 22 May 2006 18:14:24 -0400 (EDT)
  • References: <e4r7qm$mmh$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Andrew Moylan schrieb:
> 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?
> 
> Cheers,
> 
> Andrew
> 
> P.S. Apologies if I have sent this twice; my original message seems not 
> to have worked.
> 
Hi Andrew,

use ComplexExpand[]:

ComplexExpand[Arg[1+I*x]+Arg[1-I*x],TargetFunctions\[Rule]{Re,Im}]
--> 0

Assuming[a>0<b,
   FullSimplify@ComplexExpand[Arg[a+I b],TargetFunctions\[Rule]{Re,Im}]]
--> ArcTan[a,b]

Peter


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