$$x^{4}-\sqrt{2}x^{2}+1=0$$
$x=e^{\frac{7\pi i}{8}}\approx -0.923879533+0.382683432i$
$x=e^{\frac{15\pi i}{8}}\approx 0.923879533-0.382683432i$
$x=e^{\frac{9\pi i}{8}}\approx -0.923879533-0.382683432i$
$x=e^{\frac{\pi i}{8}}\approx 0.923879533+0.382683432i$
