Let a and b be real numbers. The complex number 4 - 5i is a root of the quadratic $z^2 + (a + 8i) z + (-39 + bi) = 0$. What is the other root?
I did a lot of work on hand and plugging this into the quadratic formula and with wolfram alpha but it doesn't simplify itself easily at all....anyone have any help to offer? Thanks!