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1

### 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
$$- 128{\omega ^2}$$
2

### 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
3

### 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
$${\pi \over 2}$$
4

### IIT-JEE 1986

MCQ (More than One Correct Answer)
Let $${z_1}$$ and $${z_2}$$ be complex numbers such that $${z_1}$$ $$\ne$$ $${z_2}$$ and $$\left| {{z_1}} \right| =\,\left| {{z_2}} \right|$$. If $${z_1}$$ has positive real and $${z_2}$$ has negative imaginary part, then $${{{z_1}\, + \,{z_2}} \over {{z_1}\, - \,{z_2}}}$$ may be
A
zero
B
real and positive
C
real and negative
D
purely imaginary

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Class 12