1

### IIT-JEE 1995 Screening

If $$\omega \,\left( { \ne 1} \right)$$ is a cube root of unity and $${\left( {1 + \omega } \right)^7} = A + B\,\omega$$ then $$A$$ and $$B$$ are respectively
A
0, 1
B
1, 1
C
1, 0
D
-1, 1
2

### IIT-JEE 1992

$${\rm{z }} \ne {\rm{0}}$$ is a complex number

Column I

(A) Re z = 0
(B) Arg $$z = {\pi \over 4}$$

Column II

(p) Re$${z^2}$$ = 0
(q) Im$${z^2}$$ = 0
(r) Re$${z^2}$$ = Im$${z^2}$$
A
(A) - q, (B) - p
B
(A) - p, (B) - q
C
(A) - r, (B) - p
D
(A) - p, (B) - r
3

### 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
4

### 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

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