Search Results for: complex

Question Number 98721 by mathmax by abdo last updated on 15/Jun/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{by}\:\mathrm{using}\:\mathrm{residue}\:\mathrm{theorem} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{by}\:\mathrm{using}\:\mathrm{complex}\:\mathrm{decomposition} \\ $$ Answered by mathmax…

Question Number 98638 by Ar Brandon last updated on 15/Jun/20 $$\mathrm{Le}\:\mathrm{plan}\:\mathrm{complexe}\:\mathrm{est}\:\mathrm{rapport}\acute {\mathrm{e}}\:\grave {\mathrm{a}}\:\mathrm{un}\:\mathrm{rep}\grave {\mathrm{e}re} \\ $$$$\mathrm{orthornorme}\:\mathrm{directe}\:\left(\mathrm{0},\overset{\rightarrow} {\mathrm{e}}_{\mathrm{1}} ,\overset{\rightarrow} {\mathrm{e}}_{\mathrm{2}} \right).\:\mathcal{O}\mathrm{n}\:\mathrm{note}\:\mathrm{A}\:\mathrm{et}\:\mathrm{B}\:\mathrm{les} \\ $$$$\mathrm{points}\:\mathrm{d}'\mathrm{affixes}\:\mathrm{respectives}\:\boldsymbol{\mathrm{i}},\:\mathrm{et}\:\mathrm{2}\boldsymbol{\mathrm{i}}.\:\mathrm{Soit}\:\mathrm{f},\:\mathrm{l}'\mathrm{application} \\ $$$$\mathrm{du}\:\mathrm{plan}\:\mathrm{priv}\acute {\mathrm{e}}\:\mathrm{de}\:\mathrm{A}\:\mathrm{dans}\:\mathrm{lui}-\mathrm{m}\hat…

Question Number 32203 by rahul 19 last updated on 21/Mar/18 $$\boldsymbol{{N}}{umber}\:{of}\:{solutions}\:{of}\:{the}\:{equation} \\ $$$${z}^{\mathrm{3}} +\frac{\left[\mathrm{3}\left(\overset{−} {{z}}\right)^{\mathrm{2}} \right]}{\mid{z}\mid}=\mathrm{0}\:{where}\:{z}\:{is}\:{a}\:{complex}\:{no}. \\ $$ Commented by rahul 19 last updated on…

Question Number 32181 by rahul 19 last updated on 21/Mar/18 $$\boldsymbol{{I}}{ntercept}\:{made}\:{by}\:{the}\:{circle}\: \\ $$$$\boldsymbol{{z}}\overset{−} {\boldsymbol{{z}}}+\overset{−} {\boldsymbol{{a}z}}+\boldsymbol{{a}}\overset{−} {\boldsymbol{{z}}}+\boldsymbol{{r}}=\mathrm{0}\:\boldsymbol{{o}}{n}\:{the}\:{real}\:{axis}\:{on} \\ $$$${complex}\:{plane}\:{is}\::− \\ $$ Commented by rahul 19 last…

Question Number 96021 by SmNayon11 last updated on 29/May/20 $$\mathrm{if}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{are}\:\mathrm{two}\:\mathrm{complex}\:\mathrm{number} \\ $$$$\mathrm{and}\:\mathrm{p}×\mathrm{q}=\mathrm{m}\:\:,\mathrm{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}\:. \\ $$$$ \\ $$$$\mathrm{is}\:\mathrm{there}\:\mathrm{always}\:\mathrm{exists}\:\mathrm{a}\:\:\mathrm{p}^{\frac{\mathrm{1}}{\mathrm{3}}} \:\mathrm{and}\:\mathrm{q}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\left(\mathrm{we}\:\mathrm{know}\:\mathrm{p}^{\frac{\mathrm{1}}{\mathrm{3}}} \:\mathrm{and}\:\mathrm{q}^{\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{each}\:\mathrm{has}\:\mathrm{actually}\:\right. \\ $$$$\left.\mathrm{3}\:\mathrm{values}\right) \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{p}^{\frac{\mathrm{1}}{\mathrm{3}}}…

Question Number 94080 by Rio Michael last updated on 16/May/20 $$\mathrm{3}.\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{number}\:{z}\:\mathrm{which}\:\mathrm{satisfy}\: \\ $$$$\mathrm{the}\:\mathrm{equation}\:{z}^{\mathrm{3}} \:=\:\mathrm{8}{i}\:,\:\mathrm{giving}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{form}\:{a}\:+\:{bi}\:\mathrm{where}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{real}. \\ $$ Answered by mr W last updated on…

Question Number 94081 by Rio Michael last updated on 16/May/20 $${P}\:\mathrm{is}\:\mathrm{the}\:\mathrm{point}\:\mathrm{representing}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{number} \\ $$$$\:{z}\:=\:{r}\left(\:\mathrm{cos}\:\theta\:+\:{i}\:\mathrm{sin}\:\theta\right)\:\mathrm{in}\:\mathrm{an}\:\mathrm{argand}\:\mathrm{diagram}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mid{z}−{a}\mid\mid{z}\:+\:{a}\mid\:=\:{a}^{\mathrm{2}} .\:\mathrm{Show}\:\mathrm{that}\:{P}\:\mathrm{moves}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\mathrm{whose}\:\mathrm{equation}\:\mathrm{is}\:{r}^{\mathrm{2}} \:=\mathrm{2}{a}^{\mathrm{2}} \:\mathrm{cos2}\theta.\:\mathrm{sketch}\:\mathrm{the}\:\mathrm{curve}\: \\ $$$${r}^{\mathrm{2}} \:=\:\mathrm{2}{a}^{\mathrm{2}} \:\mathrm{cos}\:\mathrm{2}\theta\:,\:\mathrm{showing}\:\mathrm{clearly}\:\mathrm{the}\:\mathrm{tangents}\:\mathrm{at}\:\mathrm{the}\:\mathrm{pole}. \\…

Question Number 92839 by i jagooll last updated on 09/May/20 $$\mathrm{let}\:\mathrm{a}\:\mathrm{is}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{such}\: \\ $$$$\mathrm{that}\:\mathrm{a}^{\mathrm{10}} \:+\:\mathrm{a}^{\mathrm{5}} \:+\mathrm{1}\:=\:\mathrm{0}. \\ $$$$\mathrm{find}\:\mathrm{a}^{\mathrm{2005}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2005}} }\:? \\ $$ Answered by john santu…

Question Number 158274 by HongKing last updated on 01/Nov/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{complex}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\left(\mathrm{1}\:+\:\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:+\:\mathrm{2}\boldsymbol{\mathrm{ix}}^{\mathrm{2}} \:+\:\left(\boldsymbol{\mathrm{i}}\:-\:\mathrm{1}\right)\boldsymbol{\mathrm{x}}\:-\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$ \\ $$ Answered by mindispower last updated on…

Question Number 25152 by tawa tawa last updated on 05/Dec/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{real}\:\mathrm{part}\:\mathrm{and}\:\mathrm{imaginary}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{number}:\:\:\:\:\mathrm{z}\:=\:\left(\mathrm{1}\:+\:\mathrm{i}\right)^{\mathrm{i}} \\ $$ Commented by tawa tawa last updated on 05/Dec/17 $$\mathrm{please}\:\mathrm{help}. \\ $$ Answered…