Axel Vogt schrieb:   
   >   
   > On 14.10.2013 20:30, clicliclic@freenet.de wrote:   
   > >   
   > > Over which extended region of complex numbers a and b does the   
   > > relation   
   > >   
   > >   ABS(a^2*ABS(b - a)^2 + ABS(a)^2*(b^2 - a^2))   
   > >   = ABS(a)*ABS(b - a)*(ABS(a)^2 + ABS(b)^2 - ABS(b - a)^2)   
   > >   
   > > hold?   
   > >   
   >   
   > Mpl:   
   >   
   >   ABS(a^2*ABS(b - a)^2 + ABS(a)^2*(b^2 - a^2))   
   >     = ABS(a)*ABS(b - a)*(ABS(a)^2 + ABS(b)^2 - ABS(b - a)^2);   
   >   eval(%, ABS = 't -> sqrt(t^2)');   
   >   solve(%);   
   >   
   >      2        2    2    2    2  2 1/2   
   >   ((a  (b - a)  + a  (-a  + b )) )    =   
   >   
   >           2 1/2         2 1/2   2    2          2   
   >         (a )    ((b - a) )    (a  + b  - (b - a) )   
   >   
   >                             {a = a, b = b}   
   >   
      
   Hmmm. ABS = 't -> sqrt(t^2)' seems to imply real arguments. And Maple's   
   result seems to imply that the relation holds for all real parameters   
   a,b. But actually it fails for a = 1, b = -1 since 4 /= -4.   
      
   Martin.   
      
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