1
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$w = {{\sqrt 3 + i} \over 2}$$ and P = { $${w^n}$$ : n = 1, 2, 3, ...}. Further and , where is the set of all complex numbers. If $${z_1} \in P \cap {H_1},\,{z_2} \in \,P \cap {H_2}$$ and 0 represents the origin, then $$\angle \,{z_1}\,o{z_2} =$$
A
$${\pi \over 2}$$
B
$${\pi \over 6}\,$$
C
$${{2\pi } \over 3}$$
D
$${{5\pi } \over 6}$$
2
IIT-JEE 2010 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $${{z_1}}$$ and $${{z_2}}$$ be two distinct complex number and let z =( 1 - t)$${{z_1}}$$ + t$${{z_2}}$$ for some real number t with 0 < t < 1. IfArg (w) denote the principal argument of a non-zero complex number w, then
A
$$\left| {z - {z_1}} \right| + \left| {z - {z_2}} \right| = \left| {{z_1} - {z_2}} \right|$$
B
Arg $$(z - {z_1})$$ = Arg$$(z - {z_2})$$
C
$$\left| {\matrix{ {z - {z_1}} & {\overline z - {{\overline z }_1}} \cr {{z_2} - {z_1}} & {{{\overline z }_2} - {{\overline z }_1}} \cr } } \right|$$ = 0
D
Arg $$(z - {z_1})$$ = Arg$$({z_2} - {z_1})$$
3
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
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
$$- 128{\omega ^2}$$
4
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
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
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