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[" For any integer "k," let "alpha_(k)=cos((k pi)/(7))+i sin((k pi)/(7))," where "i=sqrt(-1)." The value of the e "],[sum_(k=1)^(12)| alpha_(k+1)-alpha_(k)|],[sum_(k=1)^(3)| alpha_(4k-1)-alpha_(4k-2)|],[(4)]

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For any integer K , let alpha_(k)=cos((kpi)/(7))+isin((kpi)/(7))," where " i=sqrt(-1) The value of the expression (sum_(k=1)^(12)|alpha_(k+1)-alpha_(k)|)/(sum_(k=1)^(3)|alpha_(4k-1)-alpha_(4k-2)|)

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