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CAS: Concern in solution
04-16-2017, 03:38 PM (This post was last modified: 04-16-2017 05:10 PM by compsystems.)
Post: #1
CAS: Concern in solution
Hi, I have a concern when the next system is resolved for the second case (x=11/4 and y=1/4), fails, why?

cplx1:=(x^2+2*y^2)+(x*i+y*i);
cplx2:=(x*y+7)+3*i;

expr1:=(cplx1 = cplx2);

answer1 := csolve(expr1,x); →

{(1/2)*(y+√(-7*y^2+(-6*i)*y+27+12*i)-i), (1/2)*(y-√(-7*y^2+(-6*i)*y+27+12*i)-i)}

wolfram

// By property of equality of complex numbers on expr1 (a+b*i = c+d*i) <=> a=c & b=d
{(x^2+2*y^2) = (x*y+7), (x+y) = 3}

answer2 := solve({ re(expr1), im(expr1)}, {x,y}); →

{[1,2],[11/4,1/4]} // (x=1 and y=2) or (x=11/4 and y=1/4)

test for (x=1 and y=2)
subst(expr1,{x = 1,y = 2}) →
(9+3*i) = (9+3*i)
evalb(Ans) → true // Xcas cmd
but
subst(answer1(1),y=2); → 1 // x=1 // ok

test for (x=11/4 and y=1/4)
subst(expr1,{x = 11/4,y = 1/4}) →
((1/8)+(121/16)+3*i) = (123+48*i)/16
evalb(Ans) → true
but
subst(answer1(2),y=1/4.); → -2.5-i // x=-2.5-i ?? -> x = 11/4

PHP Code:
//evalBool
#cas
  
evalbexprIn ):=
  
begin
   
return( iftesubst(exprIn'=','==' ), "true""false") );
  
end;
#end 
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