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Question Number 49246 by maxmathsup by imad last updated on 04/Dec/18

simplify   Π_(k=0) ^(n−1) (e^(i((4kπ)/n))  −2cosθ e^((i2π)/n)  +1)

$${simplify}\:\:\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left({e}^{{i}\frac{\mathrm{4}{k}\pi}{{n}}} \:−\mathrm{2}{cos}\theta\:{e}^{\frac{{i}\mathrm{2}\pi}{{n}}} \:+\mathrm{1}\right) \\ $$

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