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Re: Re: Simplification and Arg[]

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  • Subject: [mg66612] Re: [mg66603] Re: [mg66593] Simplification and Arg[]
  • From: Andrzej Kozlowski <akoz at>
  • Date: Wed, 24 May 2006 03:01:47 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

On 23 May 2006, at 07:14, David Park wrote:

> Andrew,
> For doing complex algebra the BIG, BIG command is ComplexExpand.  
> One can
> hardly get along without it. But for some reason, users starting  
> out with
> complex algebra on Mathematica frequently overlook it. (Maybe they  
> should
> have called it ComplexSimplify?)

I don't think so: it quite properly called ComplexExpand because it  
"expands". In fact, for purely real expressions it will usually  
return the same output as Expand:

ComplexExpand[(a + b)*(c + d)]

a*c + b*c + a*d + b*d

On the other hand if a and b are complex, the expression returned by  
ComplexExpand will certainly in general not be simpler than the  
original one:

ComplexExpand[(a + b)*(c + d), {a, b, c, d}]

(-Im[a])*Im[c] - Im[b]*Im[c] - Im[a]*Im[d] - Im[b]*Im[d] + Re[a]*Re 
[c] + Re[b]*Re[c] + Re[a]*Re[d] + Re[b]*Re[d] +
   I*(Im[c]*Re[a] + Im[d]*Re[a] + Im[c]*Re[b] + Im[d]*Re[b] + Im[a]*Re 
[c] + Im[b]*Re[c] + Im[a]*Re[d] + Im[b]*Re[d])

I do not think I would call this "simplifying",  would you? ;-)

Andrzej Kozlowski
Tokyo, Japan

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