Complex Conjugate Root (C)

If p(z) is a polynomial with real coefficients, a and b are real numbers, and p(a+bi) = 0 then p(a-bi) = 0 as well. In this case we have z-(a+bi) and z-(a-bi) are factors, so

(z-(a+bi))(z-(a-bi)) = z² + 2az + (a² + b²)

is also a factor, and can be divided out from p(z).