Complex Numbers

Let \(\mathrm{p,q\in\mathbb{R}}\) and \({\left( {1 - \sqrt 3 i} \right)^{200}} = {2^{199}}(p + iq),i = \sqrt { - 1}\) then \(\mathrm{p+q+q^2}\) and \(\mathrm{p-q+q^2}\) are roots of the equation.