Question 41

For any integer k, let $$\alpha_k = \cos \left(\frac{k\pi}{7}\right) + i \sin \left(\frac{k\pi}{7}\right),$$ where $$i = \sqrt -1.$$ The value of the expression $$\frac{\sum_{k = 1}^{12}|\alpha_{k + 1} - \alpha_k|}{\sum_{k = 1}^{3}|\alpha_{4k - 1} - \alpha_{4k - 2}|}$$ is

Correct Answer: 4

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