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Author: Tinku Tara

Is-i-0-i-1-i-2-i-n-cyclic-for-any-value-of-n-Determine-the-smallest-such-n-if-it-exists-is-a-complex-cuberoot-of-unity-and-i-1-

Question Number 8301 by Rasheed Soomro last updated on 06/Oct/16 $$\mathrm{Is}\:\:\left\{\:\left(\omega+\mathrm{i}\right)^{\mathrm{0}} ,\:\left(\omega+\mathrm{i}\right)^{\mathrm{1}} ,\:\left(\omega+\mathrm{i}\right)^{\mathrm{2}} ,\:….,\:\left(\omega+\mathrm{i}\right)^{\mathrm{n}} \:\right\} \\ $$$$\mathrm{cyclic}\:\mathrm{for}\:\mathrm{any}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}? \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{such}\:\mathrm{n}\:\mathrm{if}\:\mathrm{it}\:\mathrm{exists}. \\ $$$$\omega\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{cuberoot}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{and} \\ $$$$\mathrm{i}=\sqrt{−\mathrm{1}} \\ $$…

Question-8300

Question Number 8300 by tawakalitu last updated on 06/Oct/16 Commented by ridwan balatif last updated on 07/Oct/16 $$\mathrm{solution} \\ $$$$\mathrm{1}.{v}=\sqrt{\mathrm{2gh}},\:\mathrm{where}\:\mathrm{h}\:\mathrm{is}\:\mathrm{height}\:\mathrm{and}\:\mathrm{g}\:\mathrm{is}\:\mathrm{gravitational}\:\mathrm{acceleration} \\ $$$$\:\:\:\:{v}=\sqrt{\mathrm{2}×\mathrm{9}.\mathrm{8}×\mathrm{5}} \\ $$$$\:\:\:\:{v}=\mathrm{9}.\mathrm{899}\:{m}/{s} \\…

by-use-Gamma-function-prove-1-0-pi-8-cos-3-4xdx-1-6-2-0-pi-sin-6-x-2-cos-8-x-2-dx-5pi-2-11-

Question Number 139371 by mohammad17 last updated on 26/Apr/21 $${by}\:{use}\:{Gamma}\:{function}\:{prove}\: \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{8}}} {cos}^{\mathrm{3}} \mathrm{4}{xdx}=\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\:\pi} {sin}^{\mathrm{6}} \left(\frac{{x}}{\mathrm{2}}\right){cos}^{\mathrm{8}} \left(\frac{{x}}{\mathrm{2}}\right){dx}=\frac{\mathrm{5}\pi}{\mathrm{2}^{\mathrm{11}}…

B-y-expessing-each-side-of-the-equation-in-terms-of-tanA-or-otherwise-show-that-sin2A-cos2A-1-sin2A-cos2A-1-tan-45-A-tanA-

Question Number 8297 by lepan last updated on 06/Oct/16 $$\underset{} {{B}y}\:{expessing}\:{each}\:{side}\:{of}\:{the} \\ $$$${equation}\:{in}\:{terms}\:{of}\:{tanA}\:,{or}\: \\ $$$${otherwise}\:{show}\:{that} \\ $$$$\frac{{sin}\mathrm{2}{A}+{cos}\mathrm{2}{A}+\mathrm{1}}{{sin}\mathrm{2}{A}+{cos}\mathrm{2}{A}−\mathrm{1}}=\frac{{tan}\left(\mathrm{45}°+{A}\right)}{{tanA}} \\ $$ Answered by Rasheed Soomro last updated…