| Jean-Marc Gulliet 2006-05-27, 10:07 pm |
| 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/mathem...s/ComplexExpand
[2] http://documents.wolfram.com/mathem...unctions/ArcTan
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