Question

If one of the vertices of the square circumscribing the circle $| z -1|=\sqrt{2}$ is $2+\sqrt{3} i$ and centroid of the triangle formed by other vertices is $k-\frac{\sqrt{3}}{3}$ i then find $k$.

Answer 1

Centroid of $\Delta BCD$
$=\left(\frac{0+0+2}{3}, \frac{\sqrt{3}+(-\sqrt{3})+(-\sqrt{3})}{3}\right)\left(\frac{2}{3},-\frac{\sqrt{3}}{3}\right)$