How do I find the quadratic equation that has -8i as a root

Answer 1

If c is a root, then x - c is a factor.

If the quadratic is to have real coefficients and if -8i is a root, then +8i must also be a root.

So, a possible quadratic with the roots -8i and 8i is (x - 8i)(x - (-8i)) = x² + 64.