If $$w=\alpha+\mathrm{i} \beta$$, where $$\beta \neq 0$$ and $$z \neq 1$$, satisfies the condition that $$\left(\frac{w-\bar{w} z}{1-z}\right)$$ is purely real, then the set of values of $$z$$ is:

If $P$ is a point on $C_1$ and $Q$ in another point on $\mathrm{C}_2$, then $\frac{\mathrm{PA}^2+\mathrm{PB}^2+\mathrm{PC}^2+\mathrm{PD}^2}{\mathrm{QA}^2+\mathrm{QB}^2+\mathrm{QC}^2+\mathrm{QD}^2}$ is equal to :

If one of the vertices of the square circumscribing the circle $$|z-1|=\sqrt{2}$$ is $$(2+\sqrt{3 i})$$. Find the other vertices of square.