z is said to be unimodular if |z|=1 . (z1-2z2)/(2-z1z2 ̅ ) is uni modular #locus of z1 #iit jee

A complex number z is said to be unimodular if |z|=1 .Suppose z1 and z2 are complex numbers such that (z1-2z2)/(2-z1z2 ̅ ) is unimodular and z_2 is not unimodular. Then the point z1 lies on a