1. The problem statement, all variables and given/known data 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 2. Relevant equations 3. The attempt at a solution I was able to prove that a=c and d=-b (I have proven they're conjugatCes) But because this is a if and only if, I must prove that if they're conjugates, then the coefficients are real. How do I do that ?