The roots of the quadratic equation x^2 + bx + c are 5 + 3i and 1 - i. What is b + c?
Recall that
If the roots of the quadratic equation x2+bx+c=0 are α and β, then α+β=−b and αβ=c. (Vieta's formula)
If the roots of the quadratic equation x2+bx+c=0 are α and β, then α+β=−b and αβ=c.
(Vieta's formula)
By this fact, we have b=−(5+3i)−(1−i)=−6−2i, c=(5+3i)(1−i)=5−2i−3i2=8−2i.
Then, b+c=−6−2i+(8−2i)=2−4i
+2729 
