JEE Advanced 2015 Paper 2 Mathematics Q1

Mathematics

Problem

For any integer

k

, let

\alpha_k=\cos\left(\dfrac{k\pi}{7}\right)+i\sin\left(\dfrac{k\pi}{7}\right)

, where

i=\sqrt{-1}

. The value of the expression

\frac{\displaystyle\sum_{k=1}^{12}|\alpha_{k+1}-\alpha_k|}{\displaystyle\sum_{k=1}^{3}|\alpha_{4k-1}-\alpha_{4k-2}|}