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Re: Abs help

  • To: mathgroup at smc.vnet.net
  • Subject: [mg42017] Re: Abs help
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Mon, 16 Jun 2003 03:58:08 -0400 (EDT)
  • References: <bc7on7$6bt$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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.
> 
> 


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