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,
A
$$z$$ lies on the imaginary axis
B
$$z$$ lies on the real axis
C
$$z$$ lies on the unit circle
D
none of these
2
IIT-JEE 1982
MCQ (Single Correct Answer)
The inequality |z-4| < |z-2| represents the region given by
A
$${\mathop{\rm Re}\nolimits} \left( z \right) \ge 0\,\,$$
B
$${\mathop{\rm Re}\nolimits} \left( z \right) < 0$$
C
$${\mathop{\rm Re}\nolimits} \left( z \right) > 0$$