$$z^{2}+(\sqrt{3+i})z+1=0$$
$z=\frac{\sqrt[4]{2}e^{\frac{3\pi i}{8}}-\sqrt{3+i}}{2}\approx -0.650113721+0.406917664i$
$z=\frac{\sqrt[4]{2}e^{\frac{11\pi i}{8}}-\sqrt{3+i}}{2}\approx -1.105203581-0.691766449i$
