Question Number 73582 by arkanmath7@gmail.com last updated on 13/Nov/19 $${Could}\:{you}\:{help}\:{me}\:{with}\:{references} \\ $$$${in}\:{complex}\:{analysis}\:{please}? \\ $$ Commented by mathmax by abdo last updated on 14/Nov/19 $${search}\:{vuibert}\:{and}\:{ellipse}\:{collection}…. \\…
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Question Number 139118 by EnterUsername last updated on 22/Apr/21 $$\mathrm{Let}\:{z}\:\mathrm{be}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}.\:\mathrm{If}\:\mid{z}+\mathrm{1}\mid=\mid{z}−\mathrm{1}\mid \\ $$$$\mathrm{and}\:\mathrm{arg}\left(\frac{{z}−\mathrm{1}}{{z}+\mathrm{1}}\right)=\frac{\pi}{\mathrm{4}}.\:\mathrm{Then}\:{z}\:\mathrm{is}\:?\: \\ $$ Answered by qaz last updated on 22/Apr/21 $$\mid{z}+\mathrm{1}\mid=\mid{z}−\mathrm{1}\mid \\ $$$$\Rightarrow{z}={a}+{bi}={bi} \\…
Question Number 139057 by EnterUsername last updated on 21/Apr/21 $$\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\mathrm{in}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{plane}\:\mathrm{satisfying} \\ $$$$\mathrm{the}\:\mathrm{inequality}\:\mathrm{log}_{\mathrm{cos}\left(\frac{\pi}{\mathrm{6}}\right)} \left[\frac{\mid\mathrm{z}−\mathrm{2}\mid+\mathrm{5}}{\mathrm{4}\mid\mathrm{z}−\mathrm{2}\mid−\mathrm{4}}\right]<\mathrm{2}\:\mathrm{is}\:? \\ $$ Answered by MJS_new last updated on 22/Apr/21 $$\mid{z}−\mathrm{2}\mid={x}\geqslant\mathrm{0} \\ $$$$\frac{\mathrm{ln}\:\frac{{x}+\mathrm{5}}{\mathrm{4}\left({x}−\mathrm{1}\right)}}{\mathrm{ln}\:\mathrm{cos}\:\frac{\pi}{\mathrm{6}}}<\mathrm{2}\:\Leftrightarrow\:\mathrm{ln}\:\frac{{x}+\mathrm{5}}{{x}−\mathrm{1}}\:>\mathrm{ln}\:\mathrm{3}…
Question Number 139052 by EnterUsername last updated on 21/Apr/21 $$\left(\mathrm{1}+\mathrm{z}\right)^{\mathrm{n}} =\left(\mathrm{1}−\mathrm{z}\right)^{\mathrm{n}} \\ $$$${where}\:{z}\:{is}\:{a}\:{complex}\:{number} \\ $$ Answered by mathmax by abdo last updated on 21/Apr/21 $$\mathrm{z}=−\mathrm{1}\:\mathrm{is}\:\mathrm{not}\:\mathrm{solution}\:\:\mathrm{let}\:\mathrm{z}\neq−\mathrm{1}…
Question Number 139055 by EnterUsername last updated on 21/Apr/21 $$\mathrm{Let}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{be}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{representing}\:\mathrm{the}\:\mathrm{points} \\ $$$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{respectively}\:\mathrm{in}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{plane}. \\ $$$$\mathrm{If}\:\frac{\mathrm{a}}{\mathrm{b}}+\frac{\mathrm{b}}{\mathrm{a}}=\mathrm{1}\:\mathrm{and}\:\mathrm{O}\:\mathrm{is}\:\mathrm{the}\:\mathrm{origin}.\:\mathrm{Then}\:\Delta\mathrm{OAB}\:\mathrm{is}\:? \\ $$ Answered by MJS_new last updated on 22/Apr/21 $$\frac{{a}}{{b}}+\frac{{b}}{{a}}=\mathrm{1}\:\Rightarrow\:{b}={a}\left(\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{i}\right) \\…
Question Number 138983 by physicstutes last updated on 20/Apr/21 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{complex}\:\mathrm{numbers}\:\mathbb{C}\:\mathrm{under}\:\mathrm{the}\:\mathrm{usual} \\ $$$$\mathrm{addition}\:\mathrm{and}\:\mathrm{multiplication}\:\mathrm{form}\:\mathrm{a}\:\mathrm{field}. \\ $$$$\left(\mathbb{C},+,×\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7748 by Tawakalitu. last updated on 13/Sep/16 $${Given}\:{that}\:{Z}\:{and}\:{H}\:{are}\:{complex}\:{number}.\: \\ $$$${obtain}\:{the}\:{real}\:{and}\:{imaginary}\:{of}\:{Z}^{{H}} \\ $$ Answered by Yozzia last updated on 13/Sep/16 $${Let}\:{Z}={re}^{{i}\theta} ,\:{H}={c}+{di}\:\:\left({r},\theta,{c},{d}\in\mathbb{R},\:{r}>\mathrm{0},\:{i}=\sqrt{−\mathrm{1}}\right). \\ $$$${Z}^{{H}}…
Question Number 7739 by upendrakishor99@gmail.com last updated on 13/Sep/16 $${Ifz}_{\mathrm{1}} ,{z}_{\mathrm{2}} {be}\:{complex}\:{numbers},\:{prove}\:{that} \\ $$$${tan}\left({z}_{\mathrm{1}} +{z}_{\mathrm{2}} \right)={tanz}_{\mathrm{1}} +{tanz}_{\mathrm{2}} /\mathrm{1}−{tanz}_{\mathrm{1}} {tanz}_{\mathrm{2}} \\ $$$$ \\ $$$$ \\ $$…
Question Number 73027 by mathmax by abdo last updated on 05/Nov/19 $${x}\:{and}\:{y}\:{are}\:{reals}\left({or}\:{complex}\right)\:{let}\:{put}\:{x}^{\left(\mathrm{0}\right)} =\mathrm{1}\:,{x}^{\left(\mathrm{1}\right)} ={x} \\ $$$${x}^{\left(\mathrm{2}\right)} ={x}\left({x}−\mathrm{1}\right)…..{x}^{\left({n}\right)} ={x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)…\left({x}−{n}+\mathrm{1}\right){prove}\:{that} \\ $$$$\left({x}+{y}\right)^{\left({n}\right)} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:\:{x}^{\left({n}−{k}\right)}…
Question Number 138539 by mohammad17 last updated on 14/Apr/21 $${find}\:{the}\:{intigral}\:{of}\:{complex}\:{number} \\ $$$$ \\ $$$${I}_{{j}} =\int_{\gamma{j}} {xdz}\:\:\:{if}\:{j}=\mathrm{1},\mathrm{2}\:{and}\:{Y}_{\mathrm{1}} {he}\:{is}\:{a}\:{circle} \\ $$$$ \\ $$$$\mid{z}\mid={R} \\ $$ Terms of…