1
IIT-JEE 1987
MCQ (More than One Correct Answer)
+2
-0.5
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
$${\pi \over 2}$$
2
IIT-JEE 1987
MCQ (More than One Correct Answer)
+2
-0.5
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 1986
MCQ (More than One Correct Answer)
+2
-0.5
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
4
IIT-JEE 1985
MCQ (More than One Correct Answer)
+2
-0.5
If $${z_1}$$ = a + ib and $${z_2}$$ = c + id are complex numbers such that $$\left| {{z_1}} \right| = \left| {{z_2}} \right| = 1$$ and $${\mathop{\rm Re}\nolimits} ({z_1}\,{\overline z _2}) = 0$$, then the pair of complex numbers $${w_1}$$ = a + ic and $${w_2}$$ = b+ id satisfies -
A
$$\left| {{w_1}} \right| = 1\,$$
B
$$\left| {{w_2}} \right| = 1\,$$
C
$${\mathop{\rm Re}\nolimits} ({w_1}\,{\overline w _2}) = 0$$
D
none of these
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