JEE Advance - Mathematics (2003 - No. 9)
If $$\,\left| z \right| = 1$$ and $$\omega = {{z - 1} \over {z + 1}}$$ (where $$z \ne - 1$$), then $${\mathop{\rm Re}\nolimits} \left( \omega \right)$$ is
0
$$ - {1 \over {{{\left| {z + 1} \right|}^2}}}$$
$$\left| {{z \over {z + 1}}} \right|.{1 \over {{{\left| {z + 1} \right|}^2}}}$$
$$\,{{\sqrt 2 } \over {{{\left| {z + 1} \right|}^2}}}$$