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Re: Re: Imaginary ...


Jesus ROJO <jesroj at wmatem.eis.uva.es>
in [mg2490] Re: [mg2430] Imaginary ...
warns about

   f:=a+I b
   Sqrt[f*Conjugate[f]]//ComplexExpand
	
      Sqrt[(a+I b) Conjugate[a+I b]]

I have recently been dealing with this laziness of ComplexExpand on  
some quite large expressions.
The following might be of interest

   ComplexExpand[Sqrt[f*Conjugate[f]],TargetFunctions ->{Re,Im}]

      Sqrt[(a - I b) (a + I b)]

Repeat:

   ComplexExpand[%,TargetFunctions ->{Re,Im}]
            2    2
       Sqrt[a  + b ]

So I used FixedPoint to automate the process

   FixedPoint[
      ComplexExpand[#, TargetFunctions ->{Re,Im}]&,
      Sqrt[f Conjugate[f]]
   ]

            2    2
      Sqrt[a  + b ]

Allan Hayes
hay at haystack.demon.co.uk


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