If the roots $\alpha$ and $\beta$ of the equation, $x^2-\sqrt2x+c=0$ are complex for some real numbers $c\ne 1$ and $|\frac{\alpha-\beta}{1-\alpha\beta}|=1$ then a value of $c$ is
Squaring both sides, I get $$(\alpha+\beta)^2-4\alpha\beta=(1-\alpha\beta)^2$$
Putting $\alpha+\beta=\sqrt2$ and $\alpha\beta=c$, I get $$c^2+2c-1=0\implies c=-1\pm\sqrt2$$.
Though, the answer is given as $3-\sqrt6$.
Also, I wonder if the roots being complex have any bearing on the solution.