Question

Find the real numbers $x$ and $y$ if $(x-iy)$ $(3+5i)$ is the conjugate of $-6-24i$.

Answer 1

Given that the expression is the conjugate of $-6-24i$

conjugate of $-6-24i$ is $-6+24i$

Hence, $(x-iy)(3+5i)$= $-6+24i$

Simplifying the expression on Left side of equlaity we get,

$3x+(5x-3y)i-5y{i}^2$ = $-6+24i$

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

Therefore,

$3x+5y$= $-6$ $\left(1\right)$

$5x-3y$ = $24$ $\left(2\right)$

solving $\left(1\right)$ and $\left(2\right)$ we get

$x=3$

$y=-3$