The roots of the quadratic equation $z^2 + bz + c = 0$ are $4 + 2i$ and $-5 + 8i$. What is $b+c$?
-b = (4 + 2i) + (-5 + 8i) = -1 + 10i
b = (1 -10i)
c = (4 + 2i) (-5 + 8i) = -20 -10i + 32i + 16i^2 = -36 +22i
b + c = (-1 + 10i) + ( -36 + 22i) = -37 + 32i
+1765 
