algebra precalculus - If the product and the sum of two complex numbers are real, what can we say about the numbers?

If the product and the sum of two complex numbers are real, what can we say about the numbers? Prove it.

Explanation will be very helpful. Actually the question asks for a proof. Hence, a proof is all that we need. I actually am quite confused with it. I have proved a lot more complex questions in complex numbers and this little proof blocked my brain. Please stop this block.

Thanks in advance!