InterviewSolution
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InterviewSolution
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For any integer k, let `alpha _h= cos. (k pi)/(7)+ I sin. (k pi)/(7) " where if "=sqrt(-1).` The value of the expression `(Sigma_(k=1)^(12) |alpha_(k+1)-alpha_k|)/(Sigma_(k=1)^(3) |alpha_(4k+1)-alpha_(4k-2)|)`is |
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Answer» Correct Answer - 4 Given `alpha_(k) = cos ((kpi)/(7)) + i sin ((k pi)/(7))` `= cos ((2k pi)/(14)) + i sin ((2 kpi)/(14))` `therefore alpha_(k)` are vertices of regular polygon having 14 sides . Let the side length of regular polygon be `alpha`. `therefore |alpha_(k + 1) - alpha_(k)| ` = length of a side of the regular polygon `= alpha " " ... (i)` and `|alpha_(4k-1) - alpha_(4k-2)|` = length of a side of the regular polygon ` = alpha " " .... (ii)` `therefore ( sum_(h=1)^(12) |alpha_(k+1) - alpha_(k)|)/(sum_(h=1)^(3) |alpha_(4k-1) - alpha_(4k-2)|) = (12(a))/(3(a)) = 4` |
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