Re: Simplification and Arg[]

• To: mathgroup at smc.vnet.net
• Subject: [mg66603] Re: [mg66593] Simplification and Arg[]
• From: "David Park" <djmp at earthlink.net>
• Date: Mon, 22 May 2006 18:14:38 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Andrew,

For doing complex algebra the BIG, BIG command is ComplexExpand. One can
hardly get along without it. But for some reason, users starting out with
complex algebra on Mathematica frequently overlook it. (Maybe they should
have called it ComplexSimplify?)

In this case one has to use the TargetFunctions option to restrict to Re and
Im.

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

David Park

From: Andrew Moylan [mailto:andrew.moylan at anu.edu.au]
To: mathgroup at smc.vnet.net

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.

```

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