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Solve-e-2z-3-i-z-x-iy-

Question Number 132834 by mohammad17 last updated on 16/Feb/21 $${Solve}\:{e}^{\mathrm{2}{z}} =\sqrt{\mathrm{3}}−{i}\:\:\:,{z}={x}+{iy} \\ $$ Answered by mathmax by abdo last updated on 20/Feb/21 $$\mid\sqrt{\mathrm{3}}−\mathrm{i}\mid=\mathrm{2}\:\Rightarrow\sqrt{\mathrm{3}}−\mathrm{i}=\mathrm{2}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{i}\right)\:=\mathrm{2e}^{−\frac{\mathrm{i}\pi}{\mathrm{6}}} =\mathrm{2e}^{\left(−\frac{\mathrm{i}\pi}{\mathrm{6}}+\mathrm{2ik}\pi\right)} \\…

Express-0-999-as-p-q-

Question Number 1736 by navajyoti.tamuli.tamuli@gmail. last updated on 04/Sep/15 $${Express}\:\mathrm{0}.\mathrm{999}…\:{as}\:\frac{{p}}{{q}} \\ $$ Answered by 123456 last updated on 04/Sep/15 $${x}=\mathrm{0}.\mathrm{999999}…. \\ $$$$\mathrm{10}{x}=\mathrm{9}.\mathrm{9999999}….. \\ $$$$\mathrm{9}{x}=\mathrm{9} \\…

dx-1-x-4-1-2-dx-1-ix-2-1-2-dx-1-ix-2-1-2-e-i-pi-4-d-e-i-pi-4-x-1-e-i-pi-4-x-2-1-2-e-i-pi-4-d-e-i-pi-4-x-1-e-i-pi-4-x-2-1-2-e-i-pi-4-ta

Question Number 132799 by Ñï= last updated on 16/Feb/21 $$\int\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} } \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{\mathrm{1}+{ix}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{\mathrm{1}−{ix}^{\mathrm{2}} } \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}{e}^{−{i}\frac{\pi}{\mathrm{4}}} \int\frac{{d}\left({e}^{{i}\frac{\pi}{\mathrm{4}}} {x}\right)}{\mathrm{1}+\left({e}^{{i}\frac{\pi}{\mathrm{4}}} {x}\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}}{e}^{{i}\frac{\pi}{\mathrm{4}}} \int\frac{{d}\left({e}^{−{i}\frac{\pi}{\mathrm{4}}} \right){x}}{\mathrm{1}+\left({e}^{−{i}\frac{\pi}{\mathrm{4}}} {x}\right)^{\mathrm{2}} }…

Question-132747

Question Number 132747 by aurpeyz last updated on 16/Feb/21 Commented by mr W last updated on 16/Feb/21 $$\frac{\mathrm{1}}{{s}}+\frac{\mathrm{1}}{{s}'}=\frac{\mathrm{2}}{{R}} \\ $$$$\frac{\mathrm{1}}{{s}}+\frac{\mathrm{1}}{−\mathrm{2}}=\frac{\mathrm{2}}{−\mathrm{12}} \\ $$$$\frac{\mathrm{1}}{{s}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\Rightarrow{s}=\mathrm{3} \\…

expand-1-x-8-

Question Number 132682 by otchereabdullai@gmail.com last updated on 15/Feb/21 $$\mathrm{expand}\:\mathrm{1}−\mathrm{x}^{\mathrm{8}} \\ $$ Answered by MJS_new last updated on 15/Feb/21 $$\mathrm{1}−{x}^{\mathrm{8}} =\left(\mathrm{1}−{x}^{\mathrm{4}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)=\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}}…