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