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1

### IIT-JEE 1983

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

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
$${\mathop{\rm Re}\nolimits} \left( z \right) > 0$$
D
none of these
3

### IIT-JEE 1982

If $$z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^5},$$ then
A
$${\mathop{\rm Re}\nolimits} \left( z \right) = 0$$
B
$${\rm I}m\left( z \right) = 0$$
C
$${\mathop{\rm Re}\nolimits} \left( z \right) > 0,\,{\rm I}m\left( z \right) > 0\,$$
D
$${\mathop{\rm Re}\nolimits} \left( z \right) > 0,\,{\rm I}m\left( z \right) < 0$$
4

### IIT-JEE 1981

The complex numbers $$z = x + iy$$ which satisfy the equation $$\,\left| {{{z - 5i} \over {z + 5i}}} \right| = 1$$ lie on
A
the x-axis
B
the straight line y=5
C
a circle passing through the origin
D
none of these

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