Question Number 113091 by bobhans last updated on 11/Sep/20 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curves} \\ $$$$\mathrm{arg}\left(\mathrm{z}\right)\:=\:\frac{\pi}{\mathrm{3}}\:;\:\mathrm{arg}\left(\mathrm{z}\right)=\:\frac{\mathrm{2}\pi}{\mathrm{3}}\:\mathrm{and}\:\mathrm{arg}\left(\mathrm{z}−\mathrm{2}−\mathrm{2i}\sqrt{\mathrm{3}}\right)=\pi \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{plane}? \\ $$ Answered by john santu last updated on 11/Sep/20 $$\:\left({i}\right)\:{arg}\:\left({z}\right)\:=\:\frac{\pi}{\mathrm{3}}\:\rightarrow\:\frac{{y}}{{x}}\:=\:\mathrm{tan}\:\left(\frac{\pi}{\mathrm{3}}\right)…
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Question Number 47523 by hassentimol last updated on 11/Nov/18 $$\mathrm{I}\:\mathrm{have}\:\mathrm{a}\:\mathrm{question}, \\ $$$$\mathrm{Can}\:\mathrm{we}\:\mathrm{consider}\:\mathrm{as}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{a} \\ $$$$\mathrm{number}\:\mathrm{if}\:\mathrm{its}\:\mathrm{real}\:\mathrm{part}\:\mathrm{or}\:\mathrm{his}\:\mathrm{imaginary} \\ $$$$\mathrm{part}\:\mathrm{is}\:\mathrm{null}\:? \\ $$$$\mathrm{For}\:\mathrm{example}\:: \\ $$$${a}\:+\:{b}\:{i} \\ $$$$\mathrm{where}\:\mathrm{a}=\mathrm{0}\:\mathrm{xor}\:\mathrm{b}=\mathrm{0}. \\ $$$$\mathrm{for}\:\mathrm{example}, \\…
Question Number 112478 by dw last updated on 08/Sep/20 $${If}\:{P}\left({x}\right)=\:{x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c},\:{with}\:{a},\:{b}\:{and}\:{c}\:{real}\:{numbers}. \\ $$$${Roots}\:{of}\:{P}\left({x}\right)\:{z}+\mathrm{3}{i},\:{z}+\mathrm{9}{i}\:{and}\:\mathrm{2}{z}−\mathrm{4},\:{find}\:\mid{a}+{b}+{c}\mid. \\ $$$$\boldsymbol{{N}}{ote}:\:{z}\:{is}\:{complex}\:{number}. \\ $$ Answered by floor(10²Eta[1]) last updated on 08/Sep/20…
Question Number 46712 by maxmathsup by imad last updated on 30/Oct/18 $${find}\:{S}\left({z}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{z}^{{n}} }{{n}^{\mathrm{2}} }\:{with}\:{z}\:{complex}\:{and}\:\mid{z}\mid=\mathrm{1}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 111159 by Rasheed.Sindhi last updated on 02/Sep/20 $${z}\:{is}\:{a}\:{complex}\:{number}\:{with}\: \\ $$$${Re}\left({z}\right)\:,\:{Im}\left({z}\right)\in\mathbb{N}. \\ $$$${Determine}\:{z}\:\:{if} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{z}.\overset{−} {{z}}=\mathrm{1000} \\ $$ Answered by Sarah85 last updated on…
Question Number 111154 by Tinku Tara last updated on 02/Sep/20 $$\mathrm{Version}\:\mathrm{2}.\mathrm{202}\:\mathrm{adds}\:\mathrm{calculator}. \\ $$$$\mathrm{place}\:\mathrm{cursor}\:\mathrm{on}\:\mathrm{a}\:\mathrm{line}\:\mathrm{which}\:\mathrm{you} \\ $$$$\mathrm{want}\:\mathrm{to}\:\mathrm{evalute}.\: \\ $$$$\mathrm{Select}\:\mathrm{calculate}\:\mathrm{from}\:\mathrm{menu}\:\mathrm{in}\:\mathrm{3}\:\mathrm{vertical} \\ $$$$\mathrm{dots}\:\mathrm{at}\:\mathrm{top}. \\ $$$$\mathrm{Calculator}\:\mathrm{accepts}\:\mathrm{complex}\:\mathrm{numbers} \\ $$$$\mathrm{and}\:\mathrm{will}\:\mathrm{return}\:\mathrm{result}\:\mathrm{in}\:\mathrm{complex} \\ $$$$\mathrm{when}\:\mathrm{needed}.…
Question Number 107690 by bemath last updated on 12/Aug/20 $$\:\:\:\:\:\:\:\:“\mathcal{B}{e}\mathcal{M}{ath}“ \\ $$$${Let}\:{the}\:{complex}\:{number}\:{z}\:{satisfies}\:{the} \\ $$$${equation}\:\mathrm{3}\left({z}−\mathrm{1}\right)=\:{i}\left({z}+\mathrm{1}\right)\: \\ $$$$\left(\mathrm{1}\right)\:{find}\:{z}\:{in}\:{the}\:{form}\:{a}+{bi}\:{where}\:{a},{b}\:\in\mathbb{R}\: \\ $$$$\left(\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\mid{z}\mid\:{and}\:\mid{z}−{z}^{\ast} \mid\: \\ $$$$ \\ $$ Answered by…
Question Number 173072 by Shrinava last updated on 06/Jul/22 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{complex}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\frac{\mid\mathrm{x}\mid^{\mathrm{2}} }{\mathrm{3}}\:\:+\:\:\frac{\mid\mathrm{y}\mid^{\mathrm{2}} }{\mathrm{5}}\:\:=\:\:\frac{\mid\mathrm{x}\:+\:\mathrm{y}\mid^{\mathrm{2}} }{\mathrm{8}}}\\{\mathrm{10x}\:\:+\:\:\mathrm{y}\:\:=\:\:\mathrm{7}\:\:+\:\:\mathrm{14}\boldsymbol{\mathrm{i}}}\end{cases} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107320 by pticantor last updated on 10/Aug/20 $${let}\:{x},{y},{z}\:{be}\:{a}\:{complex}\:{numbers} \\ $$$${as}\:\mid{x}\mid=\mid{y}\mid=\mid{z}\mid=\mathrm{1} \\ $$$$\begin{cases}{{x}+{y}+{z}=\mathrm{1}}\\{{xyz}=\mathrm{1}}\end{cases} \\ $$$${calcul}\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}=? \\ $$$$\:\:{x}=?\:{y}=?\:{z}=? \\ $$$${please}\:{i}\:{need}\:{a}\:{help} \\ $$ Commented by bemath…
Question Number 39708 by NECx last updated on 10/Jul/18 $${Find}\:{the}\:{complex}\:{number}\:{z}\:{if} \\ $$$${arg}\left({z}+\mathrm{1}\right)=\frac{\pi}{\mathrm{3}} \\ $$$${arg}\left({z}−\mathrm{1}\right)=\frac{\mathrm{4}\pi}{\mathrm{3}} \\ $$ Answered by MrW3 last updated on 10/Jul/18 $${let}\:{z}={a}+{bi} \\…