1
IIT-JEE 1985
+2
-0.5
If $$a,\,b,\,c$$ and $$u,\,v,\,w$$ are complex numbers representing the vertics of two triangles such that $$c = \left( {1 - r} \right)a + rb$$ and $$w = \left( {1 - r} \right)u + rv,$$ where $$w = \left( {1 - r} \right)u + rv,$$ is a complex number, then the two triangles
A
have the same area
B
are similar
C
are congruent
D
none of these
2
IIT-JEE 1983
+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
3
IIT-JEE 1983
+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
4
IIT-JEE 1982
+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
$${\mathop{\rm Re}\nolimits} \left( z \right) > 0,\,{\rm I}m\left( z \right) < 0$$
EXAM MAP
Medical
NEET