For any integer

MATHEMATICS · Subjective · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

For any 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} . Find the value of the expression ∑k=112∣αk+1−αk∣∑k=13∣α4k−1−α4k−2∣\frac{\sum_{k=1}^{12} |\alpha_{k+1} - \alpha_k|}{\sum_{k=1}^{3} |\alpha_{4k-1} - \alpha_{4k-2}|}.

Related theory

Browse the problem library