I have two complex numbers that are non real, $k$ and $z$. $k$ and $z$ are going to be complex conjugates if and only if the product $(x-k)(x-z)$ is a polynomial with real coefficients.

Here is my answer :

$$k=a+bi\\
z=c+di\\
(x-k)(x-z) = x^2-(k+z)x+kz$$

After that, I'm not sure what to do. I guess that I need to add $k+z$ and multiply $k\*z$.

Any hints?