Please note: two complex numbers are equal when their real parts are equal and their imaginary parts are equal.
i.e., if a+bi=c+di, then a=c and b=d
Find real numbers X and Y for which:
(X+yi)(y-i)=-4-7i
$\displaystyle (x + yi)(y - i) = xy - xi + y^2i -i^2y$
$\displaystyle xy + (y^2 - x)i + y$
$\displaystyle y(x + 1) + (y^2 - x)i$.
The real parts need to be equal, and the imaginary parts need to be equal.
So $\displaystyle y(x + 1) = -4$ and $\displaystyle y^2 - x = -7$.
Solve these equations simultaneously for $\displaystyle x$ and $\displaystyle y$.