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Re: Re: Abs help

  • To: mathgroup at smc.vnet.net
  • Subject: [mg42058] Re: [mg42017] Re: Abs help
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Tue, 17 Jun 2003 05:44:04 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

This is unnecessarily complicated:


y = Exp[I*x] + 1;


FullSimplify[ComplexExpand[Abs[y], TargetFunctions ->
     {Re, Im}]]

Sqrt[2]*Sqrt[1 + Cos[x]]


On Monday, June 16, 2003, at 04:58 PM, Dr. Wolfgang Hintze wrote:

> In my opinion, to deal with complex numbers in Mathematica is sometimes
> not very intuitive. But if we define our own Abs[]
>
> wehAbs[t_] :=
>    Sqrt[ComplexExpand[t, TargetFunctions -> {Abs, Arg}]*
>            ComplexExpand[Conjugate[t], TargetFunctions -> {Abs, Arg}]] 
> //
>        TrigExpand // Simplify
>
> then
>
> In[1]:=
> y = Exp[I*x] + 1;
>
> gives
>
> In[23]:=
> wehAbs[y]
>
> Out[23]=
> Sqrt[2]*Sqrt[1 + Cos[x]]
>
> Notice that the result differs from yours.
>
> Wolfgang
>
>
> Rex_chaos wrote:
>
>> hi all,
>>   Here is a expr
>>     y=Exp[I*x]+1;
>>   where x is REAL. I would like to take the absolute value of y
>>
>>   However, it gives
>>
>>   In[1]:=Abs[ExpToTrig[y]]^2
>>   Out[1]=Abs[1 + Cos[2 x] + \[ImaginaryI] Sin[2 x]]^2
>>
>>   How can I get the result Sin[2 x]^2 + (1+Cos[2 x])^2 ?
>>
>>   How to tell mathematica x is REAL?
>>
>> Thanks.
>>
>>
>
>
>
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/


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