$$z^{2}+(\sqrt{3}+i)z+1=0$$
$z=\sqrt{3}\left(-\frac{1}{2}+\frac{1}{2}i\right)+\left(\frac{1}{2}-\frac{1}{2}i\right)\approx -0.366025404+0.366025404i$
$z=\sqrt{3}\left(-\frac{1}{2}-\frac{1}{2}i\right)+\left(-\frac{1}{2}-\frac{1}{2}i\right)\approx -1.366025404-1.366025404i$
