For any integer k , let w_k = ( k 11 ) + i , ( k 11 ) where i = -… - Vidyadip

MCQ

For any integer $k$ , let $w_k$ = $\cos \left( {\frac{{k\pi }}{{11}}} \right) + i\,\sin \left( { \frac{{k\pi }}{{11}}} \right)$ where $i$ = $\sqrt {-1}$ . The value of the expression $\frac{{\sum\limits_{k = 1}^8 {\left| {{w_{2k + 1}} - {w_{2k}}} \right|} }}{{\sum\limits_{k = 1}^4 {\left| {{w_{3k - 1}} - {w_{3k - 2}}} \right|} }}$ is

A
$1$
✓
$2$
C
$3$
D
$4$

✓

Answer

Correct option: B.

$2$

b
$\frac{\left|w_{3}-w_{2}\right|+\left|w_{5}-w_{4}\right|+\left|w_{7}-w_{6}\right|+\ldots .+\left|w_{17}-w_{16}\right|}{\left|w_{2}-w_{1}\right|+\left|w_{5}-w_{9}\right|+\left|w_{8}-w_{7}\right|+\left|w_{11}-w_{10}\right|}$

$\therefore \quad\left|\mathrm{w}_{1}-\mathrm{w}_{2}\right|=\left|\mathrm{w}_{2}-\mathrm{w}_{3}\right|=\ldots \ldots=\mathrm{a}$

$\therefore \quad$ Ratio $=\frac{8 \mathrm{a}}{4 \mathrm{a}}=2$

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