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Author: Tinku Tara

G-x-x-1-x-3-Q-x-px-q-a-Given-that-G-x-leaves-a-remainder-of-8-and-24-when-divided-by-x-1-and-x-3-respectively-find-the-remainder-when-G-x-is-divided-by-x-1-x-3-b-Given-that-x-2-

Question Number 67299 by Rio Michael last updated on 25/Aug/19 $${G}\left({x}\right)=\:\left({x}+\mathrm{1}\right)\left({x}+\mathrm{3}\right){Q}\left({x}\right)\:+\:{px}\:+{q} \\ $$$$\left.{a}\right)\:{Given}\:{that}\:{G}\left({x}\right)\:{leaves}\:{a}\:{remainder}\:{of}\:\mathrm{8}\:{and}\:−\mathrm{24}\:{when}\:{divided}\:{by}\:\left({x}+\mathrm{1}\right)\:{and}\: \\ $$$$\left({x}+\mathrm{3}\right)\:{respectively},{find}\:{the}\:{remainder}\:{when}\:{G}\left({x}\right)\:{is}\:{divided}\:{by}\:\left({x}+\mathrm{1}\right)\left({x}+\mathrm{3}\right). \\ $$$$\left.{b}\right)\:\:{Given}\:{that}\:{x}+\mathrm{2}\:{is}\:{a}\:{factor}\:{of}\:{G}\left({x}\right)\:{and}\:{that}\:{the}\:{graph}\:{of}\:{G}\left({x}\right)\:{passes}\:{through} \\ $$$${the}\:{point}\:{with}\:{coordinates}\:\left(\mathrm{0},\mathrm{6}\right)\:{find}\:{G}\left({x}\right) \\ $$ Commented by Rasheed.Sindhi last…

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)} \\…