Question

Determinati numerele reale x,y pentru care are loc egalitatea (3-2i)x+4=(1+3i)y-2i.

Answer 1

[tex](3-2i)x+4=(1+3i)y-2i\\ 3x-2ix+4=y+3iy-2i\\ 3x-y-2ix-3iy=-4-2i\\ 3x-y+i(-2x-3y)=-4-2i\\ Obtinem\ sistemul:\\ \left \{ {{3x-y=-4} \atop {-2x-3y=-2}} \right. \Leftrightarrow \left \{ {{6x-2y=-8} \atop {-6x-9y=-6}} \right. \\ Prin\ adunare: -11y=-14\Rightarrow \boxed{y=\frac{11}{14}}\\ 3x-\frac{11}{14}=-4\\ 3x=\frac{11}{14}-4\\ 3x=-\frac{45}{14}\Rightarrow \boxed{x=-\frac{15}{14}}[/tex]