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Author: Tinku Tara

If-270-lt-x-lt-360-simplify-2-2-2cosx-

Question Number 8306 by lepan last updated on 07/Oct/16 $${If}\:\mathrm{270}°<{x}<\mathrm{360}°,\:{simplify} \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\mathrm{2}{cosx}}}. \\ $$ Commented by sou1618 last updated on 07/Oct/16 $$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\mathrm{2}{cosx}}}\:\left(\mathrm{270}°<{x}<\mathrm{360}°\right) \\ $$$$\mathrm{2}{cos}^{\mathrm{2}} \alpha=\mathrm{1}+{cos}\mathrm{2}\alpha…

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 $$\mathrm{Is}\:\:\left\{\:\left(\omega+\mathrm{i}\right)^{\mathrm{0}} ,\:\left(\omega+\mathrm{i}\right)^{\mathrm{1}} ,\:\left(\omega+\mathrm{i}\right)^{\mathrm{2}} ,\:….,\:\left(\omega+\mathrm{i}\right)^{\mathrm{n}} \:\right\} \\ $$$$\mathrm{cyclic}\:\mathrm{for}\:\mathrm{any}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}? \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{such}\:\mathrm{n}\:\mathrm{if}\:\mathrm{it}\:\mathrm{exists}. \\ $$$$\omega\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{cuberoot}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{and} \\ $$$$\mathrm{i}=\sqrt{−\mathrm{1}} \\ $$…