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Complex Numbers question

2014 · Shift 2 · Q27

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2014 · Shift 2 · Q27

Complex Numbers question

2014 · Shift 2 · Q27

JEE AdvancedMathematicsComplex NumbersMCQ+3 / −1

Let

{z_k}

=

\cos \left( {{{2k\pi } \over {10}}} \right) + i\,\,\sin \left( {{{2k\pi } \over {10}}} \right);\,k = 1,2....,9

List-I P. For each

{z_k}

= there exits as

{z_j}

such that

{z_k}

.

{z_j}

= 1 Q. There exists a

k \in \left\{ {1,2,....,9} \right\}

such that

{z_1}.z = {z_k}

has no solution z in the set of complex numbers R.

{{\left| {1 - {z_1}} \right|\,\left| {1 - {z_2}} \right|\,....\left| {1 - {z_9}} \right|} \over {10}}

equals S.

1 - \sum\limits_{k = 1}^9 {\cos \left( {{{2k\pi } \over {10}}} \right)}

equals List-II 1. True 2. False 3. 1 4. 2

A
P = 1, Q = 2, R = 4, S = 3
B
P = 2, Q = 1, R = 3, S = 4
C
P = 1, Q = 2, R = 3, S = 4
D
P =2, Q = 1, R = 4, S = 3

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