And 3 distributed on 3 plus i is equal to 9 plus 3i.

Not the principal square root, but one of the square roots of negative 1. So if I get rid of this, this is just 8 plus 6i.

Upon investigation, it was discovered that these square roots were called imaginary numbers and the roots were referred to as complex roots.

The two complex solutions are 3i and —3i. This pattern of complex conjugates will occur in every set of complex roots that you will encounter when solving a quadratic equation.

It's going to get a little bit hairy, because we're going to have to square it and all the rest.

The equation has two complex solutions.

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Quadratic Equations with Complex Solutions