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