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Re: simplify Arg[E^(I x)]?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125755] Re: simplify Arg[E^(I x)]?
  • From: Andrzej Kozlowski <akozlowski at gmail.com>
  • Date: Sun, 1 Apr 2012 03:34:45 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201203310842.DAA12986@smc.vnet.net>

The first and obvious problem is that it should be FullSimplify and not 
Fullsimplify. But fixing that won't help since your expected answer is 
incorrect. All you need to do is to look up Mathematica's help for Arg 
and you will see:

The result from Arg[z] is always between -\[Pi] and +\[Pi]

But then, it is immediately obvious that if you take an x not in this 
range than the answer is not going to be x, for example:

Arg[Exp[3 Pi/2 I]]

-(\[Pi]/2)

Also, this tells you what you have to do to get the answer you are 
looking for:

FullSimplify[Arg[Exp[I x]], -Pi < x <= Pi]

x


Andrzej Kozlowski

On 31 Mar 2012, at 10:42, Neal Becker wrote:

> Why doesn't this simplify?
>
> Fullsimplify[Arg[E^(I x)], x \[Element] Reals]
>
> I expect to get 'x'.
>
> Is there some way I can get this to simplify?
>




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