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solve-this-equation-in-all-part-of-complex-number-x-9-3x-2-1-x-6-4-x-9-3x-2-1-x-6-16-

Question Number 63383 by minh2001 last updated on 03/Jul/19 $${solve}\:{this}\:{equation}\:{in}\:{all}\: \\ $$$${part}\:{of}\:{complex}\:{number}: \\ $$$$\sqrt{\left({x}^{\mathrm{9}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}−\mathrm{6}\right)+\mathrm{4}}=\left({x}^{\mathrm{9}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}−\mathrm{6}\right)−\mathrm{16} \\ $$ Commented by MJS last updated…

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For-any-complex-number-z-z-n-z-has-n-2-solutions-How-

Question Number 128459 by SLVR last updated on 07/Jan/21 $${For}\:{any}\:{complex}\:{number}\:{z},{z}^{{n}} =\bar {{z}}\:{has}\:\left({n}+\mathrm{2}\right)\:{solutions}\:{How}??? \\ $$ Answered by mr W last updated on 10/Jan/21 $${let}\:{z}={r}\left(\mathrm{cos}\:\theta+{i}\:\mathrm{sin}\:\theta\right)={re}^{{i}\theta} \\ $$$${z}^{{n}}…

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for-any-complex-number-if-im-z-gt-0-then-im-1-z-gt-0-prove-this-

Question Number 127261 by mohammad17 last updated on 28/Dec/20 $${for}\:{any}\:{complex}\:{number}\:{if}\:{im}\left({z}\right)>\mathrm{0} \\ $$$${then}\:{im}\left(\frac{\mathrm{1}}{{z}}\right)>\mathrm{0}\:\:\:\:{prove}\:{this}\:? \\ $$ Commented by mr W last updated on 28/Dec/20 $${wrong}! \\ $$$${if}\:{im}\left({z}\right)>\mathrm{0}\:{then}\:{im}\left(\frac{\mathrm{1}}{{z}}\right)<\mathrm{0}.…

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calculus-I-complex-analysis-calculate-0-ln-x-x-2-3x-2-dx-ln-2-2-2-

Question Number 127224 by mnjuly1970 last updated on 28/Dec/20 $$\:\:…\:{calculus}\:\:\left({I}\right)\:−{complex}\:{analysis}… \\ $$$$\:\:\:\:{calculate}\:::\: \\ $$$$\:\:\Phi\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}}\:{dx}=\frac{{ln}^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by mindispower…

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if-x-y-z-are-three-distinct-complex-numbers-such-that-x-y-z-y-z-x-z-x-y-0-then-find-the-value-of-x-2-y-z-2-

Question Number 192160 by universe last updated on 10/May/23 $$\mathrm{if}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\mathrm{are}\:\mathrm{three}\:\mathrm{distinct}\:\mathrm{complex}\:\mathrm{numbers} \\ $$$$\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{x}}{\mathrm{y}−{z}}+\frac{\mathrm{y}}{\mathrm{z}−\mathrm{x}}+\frac{\mathrm{z}}{\mathrm{x}−\mathrm{y}}\:=\:\mathrm{0}\:\mathrm{then}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\Sigma\:\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{y}−\mathrm{z}\right)^{\mathrm{2}} } \\ $$ Commented by mehdee42 last updated on 09/May/23…

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z-0-and-z-is-complex-z-x-iy-with-x-y-R-Given-these-points-with-theirs-affix-0-0-0i-N-z-2-1-and-P-1-z-2-1-1-Show-that-1-z-2-1-z-2-1-z-2-1-2-1-2-2-What-is-the-nat

Question Number 126267 by mathocean1 last updated on 19/Dec/20 $${z}\neq\mathrm{0}\:{and}\:{z}\:{is}\:{complex}; \\ $$$${z}={x}+{iy}\:{with}\:{x};{y}\:\in\:\mathbb{R}^{\ast} . \\ $$$${Given}\:{these}\:{points}\:{with}\:{theirs} \\ $$$${affix}: \\ $$$$\mathrm{0}\left(\mathrm{0}+\mathrm{0}{i}\right);\:{N}\left({z}^{\mathrm{2}} −\mathrm{1}\right)\:{and}\:{P}\left(\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{2}} }−\mathrm{1}\right) \\ $$$$\mathrm{1}.\:{Show}\:{that} \\ $$$$\left(\frac{\mathrm{1}}{{z}^{\mathrm{2}}…

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Ques-1-Metric-Space-Question-Let-X-be-the-set-of-all-bounded-sequences-of-complex-numbers-That-is-every-element-of-is-a-complex-sequence-x-x-k-1-such-x-i-lt

Question Number 191786 by Mastermind last updated on 30/Apr/23 $$\mathrm{Ques}.\:\mathrm{1}\:\left(\mathrm{Metric}\:\mathrm{Space}\:\mathrm{Question}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Let}\:\mathrm{X}\:=\:\rho_{\infty} \:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\: \\ $$$$\mathrm{bounded}\:\mathrm{sequences}\:\mathrm{of}\:\mathrm{complex}\: \\ $$$$\mathrm{numbers}.\:\mathrm{That}\:\mathrm{is}\:\mathrm{every}\:\mathrm{element}\:\mathrm{of} \\ $$$$\rho_{\infty} \:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{sequence}\:\overset{−} {\mathrm{x}}=\left\{\overset{−} {\mathrm{x}}\right\}_{\mathrm{k}=\mathrm{1}} ^{\infty} \: \\…

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