Mathematics

The conjugate of $-6-24i$ is $-6+24i$, so you need to solve $(x-iy)(3+5i) = -6+24i$. The key insight is to expand the left side using FOIL, separate the real and imaginary parts, and set up a system of two equations in two unknowns. This turns a complex number equation into an algebra problem you already know how to solve.

The conjugate of $-6-24i$ is $-6+24i$, so you need to solve $(x-iy)(3+5i) = -6+24i$. The key insight is to expand the left side using FOIL, separate the real and imaginary parts, and set up a system of two equations in two unknowns. This turns a complex number equation into an algebra problem you already know how to solve.