let-a-R-z-C-resolve-z-1-n-e-ipina-deduce-that-P-n-k-0-n-1-sin-a-kpi-n-

Question Number 198357 by pticantor last updated on 18/Oct/23

let a∈R, z∈C resolve (z+1)^n =e^(iπna) deduce that P_n =Π_(k=0) ^(n−1) sin(a+((kπ)/n))

$$\boldsymbol{{let}}\:\:\boldsymbol{{a}}\in\mathbb{R},\:\boldsymbol{{z}}\in\mathbb{C} \\ $$$$\boldsymbol{{resolve}}\: \\ $$$$\left(\boldsymbol{{z}}+\mathrm{1}\right)^{\boldsymbol{{n}}} =\boldsymbol{{e}}^{\boldsymbol{{i}}\pi\boldsymbol{{na}}} \\ $$$$\boldsymbol{{deduce}}\:\boldsymbol{{that}}\:\boldsymbol{{P}}_{\boldsymbol{{n}}} =\underset{{k}=\mathrm{0}} {\overset{\boldsymbol{{n}}−\mathrm{1}} {\prod}}\boldsymbol{{sin}}\left(\boldsymbol{{a}}+\frac{\boldsymbol{{k}}\pi}{\boldsymbol{{n}}}\right) \\ $$

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let-a-R-z-C-resolve-z-1-n-e-ipina-deduce-that-P-n-k-0-n-1-sin-a-kpi-n-

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