Calculating poles with complex numbers and quadratic equation

1. How do you find the roots of a quadratic equation with complex numbers?
2. Can you use quadratic formula with complex coefficients?

How do you find the roots of a quadratic equation with complex numbers?

The complex roots of a quadratic equation with real coefficients occur in complex conjugate pairs. We use the formula x = (-b±i√(4ac – b²))/2a. So, if z = p+iq is a root of a quadratic equation with real coefficients, then the other root is z = p-iq.

Can you use quadratic formula with complex coefficients?

We can solve quadratic equations with complex coefficients using the quadratic formula. If the discriminant is zero, the equation has one repeated root. If all the coefficients are real, the root will be real. A general quadratic with complex coefficients can have any combination of real and nonreal roots.