Question Number 48227 by gunawan last updated on 21/Nov/18 $$\left(\mathrm{1}−{i}\right)^{\mathrm{4}{i}} =.. \\ $$ Answered by Smail last updated on 21/Nov/18 $$\left(\mathrm{1}−{i}\right)^{\mathrm{4}{i}} =\left(\sqrt{\mathrm{2}}\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}−{i}\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)\right)^{\mathrm{4}{i}} =\left(\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\mathrm{4}{i}} \left({e}^{−\frac{{i}\pi}{\mathrm{4}}}…
Question Number 48226 by gunawan last updated on 21/Nov/18 $$\mathrm{calculate} \\ $$$$\mathrm{log}\left(−\mathrm{1}+\sqrt{\mathrm{3}}\:\mathrm{i}\right)^{\mathrm{2}} \\ $$ Answered by Smail last updated on 21/Nov/18 $${ln}\left(\left(−\mathrm{1}+\sqrt{\mathrm{3}}{i}\right)^{\mathrm{2}} \right)=\mathrm{2}{ln}\left(\mathrm{2}\left(−\frac{\mathrm{1}}{\mathrm{2}}+{i}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)\right) \\ $$$$=\mathrm{2}{ln}\mathrm{2}+\mathrm{2}{ln}\left({cos}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)+{isin}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\right)…
Question Number 179289 by Tawa11 last updated on 27/Oct/22 A refrigerator use 1200joules of work to jump 300j of heat from a cold reservoir of…
Question Number 48208 by naka3546 last updated on 20/Nov/18 $${f}\left({x}\right)\:+\:\left({x}\:+\:\mathrm{1}\right)^{\mathrm{3}} \:\:=\:\:\mathrm{2}{f}\left({x}\:+\:\mathrm{1}\right) \\ $$$${f}\left(\mathrm{10}\right)\:\:=\:\:? \\ $$ Answered by MJS last updated on 20/Nov/18 $${f}\left({x}\right)={ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}…
Question Number 179266 by mokys last updated on 27/Oct/22 $${prove}\:{that}\:\mid{z}−{w}\mid^{\mathrm{2}} +\mid{z}\:−\:\overset{−} {{w}}\mid\:=\:\mathrm{4}\:{R}\boldsymbol{{e}}\:{z}\:{Rew} \\ $$ Commented by mokys last updated on 27/Oct/22 $$\bigstar \\ $$$$ \\…
Question Number 113714 by mathdave last updated on 14/Sep/20 Answered by Olaf last updated on 15/Sep/20 $$\mathrm{I}_{{n}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} \mathrm{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}}{dx} \\ $$$$\mathrm{I}_{\mathrm{0}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 113708 by Rasikh last updated on 15/Sep/20 $$\:\:\:\:\:\int\mathrm{x}^{\mathrm{x}} \:\mathrm{dx}\:=?\:\: \\ $$ Commented by Dwaipayan Shikari last updated on 14/Sep/20 $${Q}\:\mathrm{111558} \\ $$ Answered…
Question Number 113706 by Rasikh last updated on 15/Sep/20 $$\:\:\:\int\sqrt{\mathrm{tanx}}\:\mathrm{dx}\:=?\:\:\:\: \\ $$ Answered by MJS_new last updated on 15/Sep/20 $$\int\sqrt{\mathrm{tan}\:{x}}\:{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:{x}}\:\rightarrow\:{dx}=\mathrm{2cos}^{\mathrm{2}} \:{x}\:\sqrt{\mathrm{tan}\:{x}}\:{dt}\right] \\ $$$$=\mathrm{2}\int\frac{{t}^{\mathrm{2}}…
Question Number 179228 by mahdipoor last updated on 26/Oct/22 $${prove}\:{in}\:{right}\:{triangle}\::\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \\ $$$$−−−−−− \\ $$ Answered by a.lgnaoui last updated on 27/Oct/22 $${Aire}\:\left({S}\right){du}\:{trapeze}\left[\mathrm{ADEB}\right] \\…
Question Number 179229 by mokys last updated on 26/Oct/22 Answered by 123564 last updated on 01/Nov/22 Commented by 123564 last updated on 01/Nov/22 Commented by…