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Re: Re: Simplification and Arg[]


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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