One of the roots of
x^2 + (a - 4i) x + (29 + bi) = 0
is x = -5 - 8i, where a and b are real numbers. Enter the ordered pair (a,b).
If -5 -8i is a root so is -5 + 8i
The sum of the roots = -(a - 4i) = -a + 4i
So
-10 = -a + 4i
a = 10 + 4i
The product of the roots = 29 + bi
(-5 - 8i) (-5 + 8i) = 29 + bi
25 - 64i^2 = 29 + bi
25 + 64 = 29 + bi
89 = 29 + bi
60 = bi