1
AIEEE 2006
+4
-1
If $${z^2} + z + 1 = 0$$, where z is complex number, then value of $${\left( {z + {1 \over z}} \right)^2} + {\left( {{z^2} + {1 \over {{z^2}}}} \right)^2} + {\left( {{z^3} + {1 \over {{z^3}}}} \right)^2} + .......... + {\left( {{z^6} + {1 \over {{z^6}}}} \right)^2}$$ is
A
18
B
54
C
6
D
12
2
AIEEE 2006
+4
-1
The value of $$\sum\limits_{k = 1}^{10} {\left( {\sin {{2k\pi } \over {11}} + i\,\,\cos {{2k\pi } \over {11}}} \right)}$$ is
A
i
B
1
C
- 1
D
- i
3
AIEEE 2005
+4
-1
If $${z_1}$$ and $${z_2}$$ are two non-zero complex numbers such that $$\,\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|$$, then arg $${z_1}$$ - arg $${z_2}$$ is equal to
A
$${\pi \over 2}\,$$
B
$$- \pi$$
C
0
D
$${{ - \pi } \over 2}$$
4
AIEEE 2005
+4
-1
If the cube roots of unity are 1, $$\omega \,,\,{\omega ^2}$$ then the roots of the equation $${(x - 1)^3}$$ + 8 = 0, are
A
$$- 1, - 1 + 2\,\,\omega , - 1 - 2\,\,{\omega ^2}$$
B
$$- 1, - 1, - 1$$
C
$$- 1,1 - 2\omega ,1 - 2{\omega ^2}$$
D
$$- 1,1 + 2\omega ,1 + 2{\omega ^2}$$
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