let-give-w-k-e-i-2kpi-n-k-Z-find-the-value-of-k-0-n-1-1-2-2-w-k-

Tinku Tara June 4, 2023 Others 0 Comments

Question Number 28431 by abdo imad last updated on 25/Jan/18

let give w_k = e^(i((2kπ)/n)) k∈Z find the value of Π_(k=0) ^(n−1) (1+(2/(2−w_k ))).

$${let}\:{give}\:{w}_{{k}} =\:{e}^{{i}\frac{\mathrm{2}{k}\pi}{{n}}} \:\:\:{k}\in{Z}\:\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left(\mathrm{1}+\frac{\mathrm{2}}{\mathrm{2}−{w}_{{k}} \:}\right). \\ $$

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