1

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
$${\mathop{\rm Re}\nolimits} \left( z \right) > 0$$
D
none of these
2

IIT-JEE 1982

MCQ (Single Correct Answer)
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
$${\mathop{\rm Re}\nolimits} \left( z \right) > 0,\,{\rm I}m\left( z \right) < 0$$
3

IIT-JEE 1981

MCQ (Single Correct Answer)
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
4

IIT-JEE 1980

MCQ (Single Correct Answer)
The smallest positive integer n for which $${\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1$$ is
A
$$n = 8$$
B
$$n = 16$$
C
$$n = 12$$
D
none of these

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