JEE Advance - Mathematics (2006 - No. 15)
If $${{w - \overline w z} \over {1 - z}}$$ is purely real where $$w = \alpha + i\beta ,$$ $$\beta \ne 0$$ and $$z \ne 1,$$ then the set of the values of z is
$$\left\{ {z:\left| z \right| = 1} \right\}$$
$$\left\{ {z:z = \overline z } \right\}$$
$$\left\{ {z:z \ne 1} \right\}\,\,$$
$$\left\{ {z:\left| z \right| = 1,z \ne 1} \right\}$$