JEE Advance - Mathematics (2007 - No. 18)

If $$\left| z \right|\, =1\,and\,z\, \ne \, \pm \,1,$$ then all the values of $${z \over {1 - {z^2}}}$$ lie on

a line not passing through the origin

$$\left| z \right|\, = \,\sqrt 2 $$