1.
Let p,qRp, q \in \mathbb{R} and (13i)200=2199(p+iq)(1 - \sqrt{3}i)^{200} = 2^{199}(p + iq), i=1i = \sqrt{-1}. Then p+q+q2p + q + q^2 and pq+q2p - q + q^2 are roots of the equation: