Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Simplification and Arg[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66727] Re: Simplification and Arg[]
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sat, 27 May 2006 21:03:56 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <e4r7qm$mmh$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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

Hi Andrew,

What you need is *ComplexExpand* [1]:

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

Out[1]=
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}
 > ]

In[2]:=
ComplexExpand[Arg[a + I*b], TargetFunctions ->
    {Re, Im}]

Out[2]=
ArcTan[a, b]

In[3]:=
FullSimplify[ComplexExpand[Arg[a + I*b], {a, b},
    TargetFunctions -> {Re, Im}], {a > 0, b > 0}]

Out[3]=
        b
ArcTan[-]
        a

For the difference between Out[2] (without information on the quadrant)
and Out[3] (with information on the quadrant) see [2].

Best regards,
Jean-Marc

[1] http://documents.wolfram.com/mathematica/functions/ComplexExpand

[2] http://documents.wolfram.com/mathematica/functions/ArcTan


  • Prev by Date: Re: mathematica database link help
  • Next by Date: Re: Newbie: Rotataion2D use problem
  • Previous by thread: Re: Re: Simplification and Arg[]
  • Next by thread: Unit sphere triangulation