Question

For the real numbers x and y, if $(x-iy)(3+5i)$ is the conjugate of $-6-24i$ then find the value of $x$ and $y$.

Answer 1

$(x-iy)(3+5i)=(3x+5y)+i(5x-3y)$

It is given that $(x-iy)(3+5i)$ is the conjugate of $-6-24i$

.

$(x-iy)(3+5i)=\overline{-6-24i}$

$(3x+5y)+i(5x-3y)=-6+24i$

$3x+5y=-6$ and $5x-3y=24$

Solving these equations, we get, $x=3$ and $y=-3$.