JEE Advance - Mathematics (1983 - No. 36)
If $$z = x + iy$$ and $$\omega = \left( {1 - iz} \right)/\left( {z - i} \right),$$ then $$\,\left| \omega \right| = 1$$ implies that, in the complex plane,
$$z$$ lies on the imaginary axis
$$z$$ lies on the real axis
$$z$$ lies on the unit circle
none of these