1

### IIT-JEE 1985

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

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 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
4

### 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

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