Question

The quadratic equation x2 + mx + q = 0, where m and q are real numbers, has the complex root a + bi.?

Answer 1

Remember the quadratic formula determinant?
If b^2 -4ac < 0, a complex root exists.

So for this problem, m^2 - 4q is the determinant, and if less than 0, is complex.

So a=-m/2   and b=(1/2)SQRT(m^2 - 4q)