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Category: Algebra

Suggested-solution-method-to-question-203502-ze-z-1-Obviously-the-only-real-solution-is-z-W-1-567143290-z-a-bi-b-0-a-bi-e-a-bi-1-a-bi-cos-b-isin-b-e-a-1-e-a-acos-b-bsin-b-e-a-asin-b-

Question Number 203570 by Frix last updated on 22/Jan/24 $$\mathrm{Suggested}\:\mathrm{solution}\:\mathrm{method}\:\mathrm{to} \\ $$$$\mathrm{question}\:\mathrm{203502} \\ $$$$ \\ $$$${z}\mathrm{e}^{{z}} =\mathrm{1} \\ $$$$\mathrm{Obviously}\:\mathrm{the}\:\mathrm{only}\:\mathrm{real}\:\mathrm{solution}\:\mathrm{is} \\ $$$${z}={W}\left(\mathrm{1}\right)\approx.\mathrm{567143290} \\ $$$$ \\ $$$${z}={a}+{b}\mathrm{i}\wedge{b}\neq\mathrm{0}…

z-4-4z-3-6z-2-4z-1-z-4-4z-3-6z-2-4z-1-z-1-z-1-Find-z-R-

Question Number 203474 by ajfour last updated on 20/Jan/24 $$\frac{{z}^{\mathrm{4}} +\mathrm{4}{z}^{\mathrm{3}} −\mathrm{6}{z}^{\mathrm{2}} −\mathrm{4}{z}+\mathrm{1}}{{z}^{\mathrm{4}} −\mathrm{4}{z}^{\mathrm{3}} −\mathrm{6}{z}^{\mathrm{2}} +\mathrm{4}{z}+\mathrm{1}}=\frac{{z}+\mathrm{1}}{{z}−\mathrm{1}} \\ $$$${Find}\:{z}\in\mathbb{R}. \\ $$ Answered by Rasheed.Sindhi last updated…

x-4-cx-d-0-then-find-p-from-p-6-4-d-3-c-4-1-3-p-2-1-0-x-c-1-3-2-p-p-2-8-p-

Question Number 203497 by ajfour last updated on 20/Jan/24 $${x}^{\mathrm{4}} +{cx}+{d}=\mathrm{0} \\ $$$${then}\:\:{find}\:{p}\:\:{from} \\ $$$${p}^{\mathrm{6}} −\mathrm{4}\left(\frac{{d}^{\:\mathrm{3}} }{{c}^{\mathrm{4}} }\right)^{\mathrm{1}/\mathrm{3}} {p}^{\mathrm{2}} −\mathrm{1}=\mathrm{0} \\ $$$${x}=\frac{{c}^{\mathrm{1}/\mathrm{3}} }{\mathrm{2}}\left({p}\pm\sqrt{−{p}^{\mathrm{2}} −\frac{\mathrm{8}}{{p}}}\:\right) \\…

Question-203416

Question Number 203416 by Spillover last updated on 18/Jan/24 Answered by a.lgnaoui last updated on 19/Jan/24 $$\:\: \\ $$$$\:\:\:\boldsymbol{\mathrm{R}}=\mathrm{2}\boldsymbol{\mathrm{r}}+\boldsymbol{\mathrm{BM}}\mathrm{cos}\:\boldsymbol{\alpha}\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\boldsymbol{\mathrm{BM}}\mathrm{sin}\:\boldsymbol{\alpha}=\boldsymbol{\mathrm{r}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$\: \\ $$$$\Rightarrow\:\:\begin{cases}{\mathrm{cos}\:\boldsymbol{\alpha}=\frac{\boldsymbol{\mathrm{R}}−\mathrm{2}\boldsymbol{\mathrm{r}}}{\boldsymbol{\mathrm{BM}}}}\\{\mathrm{sin}\:\boldsymbol{\alpha}=\frac{\boldsymbol{\mathrm{r}}}{\:\boldsymbol{\mathrm{BM}}}}\end{cases}…

If-z-iz-2-13-and-z-1-x-1-i-Find-mun-x-

Question Number 203417 by hardmath last updated on 18/Jan/24 $$\mathrm{If} \\ $$$$\mid\overline {−\mathrm{z}\:+\:\boldsymbol{\mathrm{i}}\mathrm{z}}\mid\:=\:\mathrm{2}\:\sqrt{\mathrm{13}}\:\:\:\mathrm{and}\:\:\:\mathrm{z}\:=\:\mathrm{1}\:+\:\left(\mathrm{x}\:+\:\mathrm{1}\right)\centerdot\boldsymbol{\mathrm{i}} \\ $$$$ \\ $$$$\mathrm{Find}:\:\:\:\mathrm{mun}\left(\mathrm{x}\right)\:=\:? \\ $$ Commented by hardmath last updated on…