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/