$d$ and $g$ are complex numbers and $g$ is not eqaul to $0$. Prove that if the roots of the equation $$x^2 + dx + g^2 = 0$$ have the same absolute value, then $d/g$ is a real number.
I tried to solve the problem by finding the roots and then transforming the results into the form of $d/g$. But it seems that I am going in the wrong direction.
Could somebody tell as to how the problem could be solved?