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Complex Numbers question

2015 · Shift 2 · Q22

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2015 · Shift 2 · Q22

Complex Numbers question

2015 · Shift 2 · Q22

JEE AdvancedMathematicsComplex NumbersNumerical+4 / −1

For any integer k, let

{a_k} = \cos \left( {{{k\pi } \over 7}} \right) + i\,\,\sin \left( {{{k\pi } \over 7}} \right)

, where

i = \sqrt { - 1} \,

. The value of the expression

{{\sum\limits_{k = 1}^{12} {\left| {{\alpha _{k + 1}} - {a_k}} \right|} } \over {\sum\limits_{k = 1}^3 {\left| {{\alpha _{4k - 1}} - {\alpha _{4k - 2}}} \right|} }}

is

Numerical answer

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