let-give-w-e-i-2pi-n-and-Z-k-0-n-1-w-k-2-find-Z-2-in-form-of-double-sum-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 28166 by abdo imad last updated on 21/Jan/18

let give w= e^(i((2π)/n)) and Z= Σ_(k=0) ^(n−1) w^k^2 find ∣Z∣^2 in form of double sum.

$${let}\:{give}\:{w}=\:{e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:\:\:\:{and}\:\:{Z}=\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{w}^{{k}^{\mathrm{2}} } \:\:\:{find}\:\mid{Z}\mid^{\mathrm{2}} \:{in} \\ $$$${form}\:{of}\:{double}\:{sum}. \\ $$

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let-give-w-e-i-2pi-n-and-Z-k-0-n-1-w-k-2-find-Z-2-in-form-of-double-sum-

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