Question Number 140444 by EnterUsername last updated on 07/May/21 $$\mathrm{If}\:\mathrm{the}\:\mathrm{points}\:\mathrm{1}+\mathrm{2}{i}\:\mathrm{and}\:−\mathrm{1}+\mathrm{4}{i}\:\mathrm{are}\:\mathrm{reflections}\:\mathrm{of} \\ $$$$\mathrm{each}\:\mathrm{other}\:\mathrm{in}\:\mathrm{the}\:\mathrm{line}\:{z}\left(\mathrm{1}+{i}\right)+\bar {{z}}\left(\mathrm{1}−{i}\right)+{K}=\mathrm{0},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{K}\:\mathrm{is}\:\_\_\_\_\_. \\ $$ Answered by mr W last updated on 08/May/21…
Question Number 140446 by EnterUsername last updated on 07/May/21 $$\mathrm{If}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{vertices}\:{Z}_{\mathrm{1}} ,\:{Z}_{\mathrm{2}} \:\mathrm{and}\:{Z}_{\mathrm{3}} \:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{absolute}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\lambda{i}\:\:\begin{vmatrix}{{Z}_{\mathrm{1}} }&{\bar {{Z}}_{\mathrm{1}} }&{\mathrm{1}}\\{{Z}_{\mathrm{2}} }&{\bar {{Z}}_{\mathrm{2}} }&{\mathrm{1}}\\{{Z}_{\mathrm{3}} }&{\bar {{Z}}_{\mathrm{3}}…
Question Number 140443 by EnterUsername last updated on 07/May/21 $$\mathrm{If}\:{z}_{\mathrm{2}} /{z}_{\mathrm{1}} \:\mathrm{is}\:\mathrm{purely}\:\mathrm{imaginary}\:\mathrm{and}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{non}-\mathrm{zero}\:\mathrm{real} \\ $$$$\mathrm{numbers},\:\mathrm{then}\:\mid\left({az}_{\mathrm{1}} +{bz}_{\mathrm{2}} \right)/\left({az}_{\mathrm{1}} −{bz}_{\mathrm{2}} \right)\mid\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\_\_\_\_\_. \\ $$ Answered by mr W last…
Question Number 9367 by tawakalitu last updated on 02/Dec/16 $$\mathrm{Solve}\:\mathrm{simultaneously}. \\ $$$$\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{4xy}\:+\:\mathrm{3y}^{\mathrm{2}} \:=\:\mathrm{3}\:\:\:………\:\left(\mathrm{i}\right) \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{3x}\:+\:\mathrm{3y}\:=\:\mathrm{4}\:\:\:\:…….\:\left(\mathrm{ii}\right) \\ $$ Answered by mrW last updated…
Question Number 140442 by EnterUsername last updated on 07/May/21 $$\mathrm{If}\:{z}_{\mathrm{1}} \:\mathrm{and}\:{z}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\:\mid{z}_{\mathrm{2}} \mid\neq\mathrm{1}\:\mathrm{and} \\ $$$$\mid\left({z}_{\mathrm{1}} −\mathrm{2}{z}_{\mathrm{2}} \right)/\left(\mathrm{2}−{z}_{\mathrm{1}} \bar {{z}}_{\mathrm{2}} \right)\mid=\mathrm{1},\:\mathrm{then}\:\mid{z}_{\mathrm{1}} \mid\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\_\_\_\_\_. \\ $$ Answered by…
Question Number 74900 by chess1 last updated on 03/Dec/19 Commented by chess1 last updated on 03/Dec/19 $$\mathrm{solve}\:\mathrm{equation} \\ $$ Commented by MJS last updated on…
Question Number 140430 by ajfour last updated on 07/May/21 $$\left(\mathrm{1}+\mathrm{2}{x}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{4}} +{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$=\left\{\left({x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)\right. \\ $$$$\left.\:\:\:\:\:\:\:−{x}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{2}{x}\right)\left({x}+\mathrm{3}\right)\right\}^{\mathrm{2}} \\ $$$${Any}\:{good}\:{non}-{zero}\:{real}\:{solution} \\…
Question Number 9349 by Yozzias last updated on 02/Dec/16 $$\mathrm{We}\:\mathrm{know}\:\mathrm{that}\:\mathbb{R}=\mathbb{Q}\cup\overset{−} {\mathbb{Q}}\:\subset\:\mathbb{C}.\:\mathrm{Is}\:\mathrm{there}\: \\ $$$$\mathrm{another}\:\mathrm{set}\:\mathbb{V}\:\mathrm{such}\:\mathrm{that}\:\mathbb{C}\subset\mathbb{V}\:? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140417 by mathsuji last updated on 07/May/21 $${if}\:{minimum}\:{value}\:{of} \\ $$$${g}\left({a};{b}\right)=\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{10}{a}−\mathrm{10}{b}+\mathrm{50}}+\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{y}+\mathrm{20}}+ \\ $$$$+\sqrt{{a}^{\mathrm{2}} −\mathrm{14}{a}+\mathrm{74}} \\ $$$${is}\:{n}\:{and}\:{occurs}\:{at}\:{a}=\gamma\:,\:{b}=\delta,\:{the}\:{find} \\ $$$$\left({n}+\mathrm{4}\gamma+\mathrm{3}\delta\right)=? \\ $$ Answered…
Question Number 74880 by aliesam last updated on 03/Dec/19 $${solve}\:{inR} \\ $$$$\sqrt[{\mathrm{5}}]{\mid{x}+\mathrm{1}\mid}−\sqrt[{\mathrm{10}}]{{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{9}}=\left(\mathrm{2}{x}−\mathrm{10}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$ Answered by mind is power last updated on 03/Dec/19…