1
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
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 1983
MCQ (Single Correct Answer)
+1
-0.25
The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order if and only if
A
z1 + z4 = z2 + z3
B
z1 + z3 = z2 + z4
C
z1 + z2 = z3 + z4
D
None of these
3
IIT-JEE 1982
MCQ (Single Correct Answer)
+2
-0.5
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 1982
MCQ (Single Correct Answer)
+2
-0.5
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
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