1
IIT-JEE 1995 Screening
+2
-0.5
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 1995 Screening
+2
-0.5
Let $$z$$ and $$\omega$$ be two complex numbers such that
$$\left| z \right| \le 1,$$ $$\left| \omega \right| \le 1$$ and $$\left| {z + i\omega } \right| = \left| {z - i\overline \omega } \right| = 2$$ then $$z$$ equals
A
$$1$$ or $$i$$
B
$$i$$ or $$-i$$
C
$$1$$ or $$- 1$$
D
$$i$$ or $$- 1$$
3
IIT-JEE 1995 Screening
+2
-0.5
Let $$z$$ and $$\omega$$ be two non zero complex numbers such that
$$\left| z \right| = \left| \omega \right|$$ and $${\rm A}rg\,z + {\rm A}rg\,\omega = \pi ,$$ then $$z$$ equals
A
$$\omega$$
B
$$- \omega$$
C
$$\overline \omega$$
D
$$- \overline \omega$$
4
IIT-JEE 1992
+2
-0.5
$${\rm{z }} \ne {\rm{0}}$$ 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
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