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Question Number 208398 by mokys last updated on 14/Jun/24 $${write}\:{z}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}+{i}}\:{in}\:{e}^{{i}\theta} \\ $$ Answered by A5T last updated on 14/Jun/24 $${z}=\frac{\sqrt{\mathrm{3}}−{i}}{\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} −\left({i}\right)^{\mathrm{2}} }=\frac{\sqrt{\mathrm{3}}−{i}}{\mathrm{4}},\:\mid{z}\mid=\sqrt{\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}\right)^{\mathrm{2}} +\left(\frac{−\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{4}} \\…

Question Number 208354 by kgmxdd last updated on 13/Jun/24 Commented by Frix last updated on 13/Jun/24 $$=\frac{\mathrm{4}}{\pi}!!! \\ $$$$\left(\mathrm{I}\:\mathrm{found}\:\mathrm{this}\:\mathrm{online}.\right) \\ $$ Terms of Service Privacy…

Question Number 208318 by SANOGO last updated on 11/Jun/24 $${calcul}\:\:\:{lim}\:{n}\rightarrow+\infty \\ $$$$\int_{\mathrm{0}} ^{+\infty} \:\frac{{cos}\left({nx}\right)}{\left({nx}+\mathrm{1}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\:}{dx} \\ $$ Answered by Berbere last updated on 11/Jun/24 $$\mid\int_{\mathrm{0}}…

Question Number 208251 by yaslm last updated on 09/Jun/24 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 208215 by MATHEMATICSAM last updated on 07/Jun/24 $$\mathrm{If}\:\frac{\mathrm{1}}{\mathrm{R}}\:=\:\frac{\mathrm{1}}{\mathrm{R}_{\mathrm{1}} }\:+\:\frac{\mathrm{1}}{\mathrm{R}_{\mathrm{2}} }\:\left[\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} \:>\:\mathrm{0}\right]\:\mathrm{and}\: \\ $$$$\mathrm{R}_{\mathrm{1}} \:+\:\mathrm{R}_{\mathrm{2}} \:=\:\mathrm{C}\:\left(\mathrm{Constant}\right)\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{R}\:\mathrm{will}\:\mathrm{be}\:\mathrm{maximum}\:\mathrm{when}\:\mathrm{R}_{\mathrm{1}} \:=\:\mathrm{R}_{\mathrm{2}} . \\ $$ Answered…