Search Results for: complex

Question Number 55672 by gunawan last updated on 01/Mar/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{complex}\:\mathrm{integral} \\ $$$$\int_{\mid{z}\mid=\mathrm{1}} \left({z}^{\mathrm{2}} \mathrm{sin}\:\frac{\mathrm{1}}{{z}}+\frac{\mathrm{1}}{{z}^{\mathrm{2}} }\mathrm{sin}\:{z}\right)\:{dz}\:\mathrm{is}… \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 186540 by akuba last updated on 05/Feb/23 $${Complex}\:{Numbers} \\ $$$${Prove}\:{that} \\ $$$$\:\mathrm{1}.\:\mid{Z}_{\mathrm{1}} +{Z}_{\mathrm{2}} \mid\leq\mid{Z}_{\mathrm{1}} \mid+\mid{Z}_{\mathrm{2}} \mid \\ $$$$\mathrm{2}.\:\mid{Z}_{\mathrm{1}} −{Z}_{\mathrm{2}} \mid\geq\mid{Z}_{\mathrm{1}} \mid−\mid{Z}_{\mathrm{2}} \mid \\…

Question Number 120151 by mathocean1 last updated on 29/Oct/20 $$\mathrm{Represent}\:\mathrm{in}\:\mathrm{complex}\:\mathrm{plane}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points} \\ $$$$\mathrm{M}\:\mathrm{which}\:\mathrm{have}\:\mathrm{as}\:\mathrm{affix}\:\mathrm{z}\:\mathrm{such}\:\mathrm{that}\:\mid\mathrm{z}\mid=\mathrm{2}\:\mathrm{and} \\ $$$$\mathrm{arg}\left(\mathrm{z}+\mathrm{1}\right)=\frac{\pi}{\mathrm{4}}\left[\pi\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 185401 by Mastermind last updated on 21/Jan/23 $$\mathrm{Show}\:\mathrm{that}\:\frac{\mathrm{1}+\mathrm{z}}{\mathrm{1}−\mathrm{z}}\:+\:\frac{\mathrm{1}+\bar {\mathrm{z}}}{\mathrm{1}−\bar {\mathrm{z}}}\:=\:\frac{\mathrm{2}\left(\mathrm{1}−\mid\mathrm{z}\mid^{\mathrm{2}} \right)}{\mid\mathrm{1}−\mathrm{z}\mid^{\mathrm{2}} } \\ $$$$\mathrm{Where}\:\mathrm{z}\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$ Commented…

Question Number 185371 by Mastermind last updated on 20/Jan/23 $$\left(\mathrm{1}−\mathrm{z}\right)\left(\mathrm{1}−\overset{−} {\mathrm{z}}\right)\:=\:? \\ $$$$\mathrm{Where}\:\mathrm{z}\:\mathrm{is}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{number} \\ $$$$ \\ $$$$. \\ $$ Answered by Frix last updated on…

Question Number 184555 by Shrinava last updated on 08/Jan/23 $$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of} \\ $$$$\mathrm{complex}\:\mathrm{numbers}\:\:\boldsymbol{\mathrm{x}}\:\mathrm{or}\:\boldsymbol{\mathrm{y}}\:\mathrm{is}\:\mathrm{7}\:,\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{cubes}\:\mathrm{is}\:\mathrm{10}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{largest} \\ $$$$\mathrm{true}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sum}\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\:\:\mathrm{that}\:\mathrm{satisfies} \\ $$$$\mathrm{these}\:\mathrm{conditions}. \\ $$$$\left.\mathrm{A}\left.\right)\left.\mathrm{4}\left.\:\left.\:\:\mathrm{B}\right)\mathrm{5}\:\:\:\mathrm{C}\right)\mathrm{6}\:\:\:\mathrm{D}\right)\mathrm{7}\:\:\:\mathrm{E}\right)\mathrm{8} \\ $$ Commented by mr…

Question Number 53455 by hassentimol last updated on 22/Jan/19 $$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{derivative} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{function}\:\mathrm{involving}\:\mathrm{complex} \\ $$$$\mathrm{numbers}\:?\:{Thanks} \\ $$ Commented by ajfour last updated on 22/Jan/19 $${study}\:{from}\:{Erwin}\:{Kreizig}'{s} \\…

Question Number 183667 by Mastermind last updated on 28/Dec/22 $$\mathrm{If}\:\mathrm{w}\:\mathrm{is}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{cube}\: \\ $$$$\mathrm{roots}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{a}+\mathrm{wb}+\mathrm{w}^{\mathrm{2}} \mathrm{c}\right)\left(\mathrm{a}+\mathrm{w}^{\mathrm{2}} \mathrm{b}+\mathrm{wc}\right)\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\left(\alpha^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} −\mathrm{ab}−\mathrm{bc}−\mathrm{c}\alpha\right). \\ $$$$ \\ $$$$…

Question Number 52498 by Joel578 last updated on 09/Jan/19 $$\mathrm{Let}\:{z}\:\mathrm{is}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{and}\:\mathrm{satisfy}\:{z}^{\mathrm{2017}} \:=\:\mathrm{1},\:\:{z}\:\neq\:\mathrm{1} \\ $$$$\mathrm{Find}\:\left(\mathrm{1}\:+\:{z}\right)\left(\mathrm{1}\:+\:{z}^{\mathrm{2}} \right)\left(\mathrm{1}\:+\:{z}^{\mathrm{3}} \right)\ldots\left(\mathrm{1}\:+\:{z}^{\mathrm{2016}} \right) \\ $$ Commented by mr W last updated on…

Question Number 52240 by aghoelvis511@gmail.com last updated on 05/Jan/19 $${i}={what}\:{in}\:{complex}\:{number}. \\ $$ Commented by Tawa1 last updated on 05/Jan/19 $$\boldsymbol{\mathrm{i}}\:\:=\:\:\boldsymbol{\mathrm{iota}} \\ $$$$ \\ $$$$\boldsymbol{\mathrm{i}}\:\:=\:\:\boldsymbol{\mathrm{cos}}\:\frac{\pi}{\mathrm{2}}\:+\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{sin}}\:\frac{\pi}{\mathrm{2}} \\…