JEE-Advanced 2015 (21/40)

Algebra Level 3

k=112αk+1αkk=13α4k1α4k2\dfrac{\displaystyle \sum_{k=1}^{12} |\alpha_{k+1}-\alpha_k|}{\displaystyle \sum_{k=1}^3 |\alpha_{4k-1}-\alpha_{4k-2}|}

For integer kk, let αk=cos(kπ7)+isin(kπ7)\alpha_k=\cos \left( \frac{k \pi}{7} \right)+i \sin \left( \frac{k \pi}{7} \right), where i=1i=\sqrt{-1}. Evaluate the value of the expression above.

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