Question

If $(x-iy)(3+5i)$ is the conjugate of $(-6-24i),$ where $x,y\in R$, then the value of $x-y$ is

Answer 1

Given : $(x-iy)(3+5i)=\overline{(-6-24i)}$
$\Rightarrow (x-iy)(3+5i)=-6+24i\Rightarrow (3x+5y)+i(5x-3y)=-6+24i\Rightarrow 3x+5y=-6,5x-3y=24\Rightarrow x=3,y=-3\therefore x-y=6$