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Re: Re: Complex Oddity

• To: mathgroup at smc.vnet.net
• Subject: [mg57650] Re: [mg57631] Re: Complex Oddity
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Fri, 3 Jun 2005 05:33:31 -0400 (EDT)
• References: <d79enu$lbl$1@smc.vnet.net><d7hahj$3q6$1@smc.vnet.net> <200506020917.FAA11965@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On Jun 2, 2005, at 5:17 AM, jfeth at azlink.com wrote:

> f=E^(I*d)
>
> In[1]:=
> f*Conjugate[f]
>
> Out[1]=
>  E^ (I*d - I*Conjugate[d])
>
> In[2]:=
> Intensity[expr_]:=
> TrigReduce[ExpToTrig[expr*TrigToExp[ComplexExpand[Conjugate 
> [ExpToTrig[expr]]]]]]
>
> In[3]:=
> Intensity[f]
>
> Out[3]=
> 1
>

In Mathematica 5.0 I get

In[1]:=
ComplexExpand[E^(I d) Conjugate[E^(I d)]]
Out[1]=
1
In[4]:=
f = E^(I d);
ComplexExpand[f Conjugate[f]]
Out[5]=
1

Is the actual expression you're working with different?


> 1) exactly what mathematical elegance (or utility)
> is gained by Mathematica's assumption that every variable is always
> complex

Because that's the most general case and the most general case is  
always mathematically appropriate while the special cases require the  
user to identify that the case is special.  Substituting values into  
the general expression will result in the same value as the special  
case anyway so there is no problem.

> 2) why there is apparently no way in Mathematica to
> globally define a variable as a real number (i.e., its own conjugate).

This actually comes up in the mailing list pretty frequently (http:// 
forums.wolfram.com/mathgroup/search/?q=define+variable 
+real&restrict=MathGroup&x=0&y=0). Here is a pretty good answer  
http://forums.wolfram.com/mathgroup/archive/1999/Nov/msg00163.html.

Regards,

Ssezi

• References:
  • Re: Complex Oddity
    • From: jfeth@azlink.com