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1

IIT-JEE 1998

MCQ (More than One Correct Answer)
The value of the sum $$\,\,\sum\limits_{n = 1}^{13} {({i^n}} + {i^{n + 1}})$$ , where i = $$\sqrt { - 1} $$, equals
A
i
B
i - 1
C
- i
D
0
2

IIT-JEE 1998

MCQ (More than One Correct Answer)
If $${\omega}$$ is an imaginary cube root of unity, then $${(1\, + \omega \, - {\omega ^2})^7}$$ equals
A
$$128\omega $$
B
$$ - 128\omega $$
C
$$128{\omega ^2}$$
D
$$ - 128{\omega ^2}$$
3

IIT-JEE 1987

MCQ (More than One Correct Answer)
The value of $$\sum\limits_{k = 1}^6 {(\sin {{2\pi k} \over 7}} - i\,\cos \,{{2\pi k} \over 7})$$ is
A
- 1
B
0
C
- i
D
i
4

IIT-JEE 1987

MCQ (More than One Correct Answer)
If $${{{z_1}}}$$ and $${{{z_2}}}$$ are two nonzero 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
$$ - \pi $$
B
$$ - {\pi \over 2}$$
C
0
D
$${\pi \over 2}$$

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