Question Number 138829 by 676597498 last updated on 18/Apr/21 Answered by physicstutes last updated on 19/Apr/21 $${T}:\:{z}\rightarrow\omega\:\Rightarrow\:\omega\:=\:\mathrm{3}{z}\:+\:\mathrm{2}−\mathrm{5}{i} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{This}\:\mathrm{transformation}\:\mathrm{is}\:\mathrm{an}\:\mathrm{enlargment}\:\mathrm{of}\:\mathrm{scale}\:\mathrm{factor}\:\mathrm{3}\:\mathrm{followed}\:\mathrm{by}\: \\ $$$$\mathrm{a}\:\mathrm{translation}\:\mathrm{of}\:\left(\mathrm{2},−\mathrm{5}\right). \\ $$$$\left(\mathrm{b}\right)\:\mathrm{For}\:\mathrm{invariant}\:\mathrm{point},\:{f}\left({z}\right)={z} \\ $$$$\Rightarrow\:\:\:{z}\:=\:\mathrm{3}{z}+\:\mathrm{2}−\mathrm{5}{i}\:\:\Rightarrow\:{z}\:=\:−\mathrm{1}+\:\frac{\mathrm{5}}{\mathrm{2}}{i}…
Question Number 7752 by Tawakalitu. last updated on 14/Sep/16 $${If}\:{f}\left({x}\right)\:=\:{x}\:+\:{ax}^{\mathrm{2}} \:+\:{bx}^{\mathrm{3}} \:+\:…\:\:\:\:\:\:.{obtain}\:\sqrt{{f}\left({x}^{\mathrm{3}} \right)} \\ $$$${up}\:{to}\:{x}^{\mathrm{3}} \\ $$ Commented by FilupSmith last updated on 14/Sep/16 $${f}\left({x}\right)={x}^{\mathrm{1}}…
Question Number 73261 by mathmax by abdo last updated on 09/Nov/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \left({n}^{\mathrm{4}} +\mathrm{2}{n}^{\mathrm{2}} −\mathrm{3}\right)\frac{{x}^{{n}} }{{n}!}\:{in}\:{case}\:{of}\:{convergence}. \\ $$ Commented by mathmax by abdo last…
Question Number 73243 by mathmax by abdo last updated on 09/Nov/19 $${prove}\:{that}\:\:{for}\:{z}\:\in{C}\:\:\:{arctanz}\:=\frac{\mathrm{1}}{\mathrm{2}{i}}{ln}\left(\frac{\mathrm{1}+{iz}}{\mathrm{1}−{iz}}\right) \\ $$$$ \\ $$ Answered by mr W last updated on 09/Nov/19 $${let}\:\mathrm{tan}^{−\mathrm{1}}…
Question Number 73227 by mathmax by abdo last updated on 08/Nov/19 $${find}\:{the}\:{polynom}\:{T}_{{n}} \:{wich}\:{verify}\:{T}_{{n}} \left({cos}\theta\right)={cos}\left({n}\theta\right) \\ $$$$\forall{n}\:{integr}\:\forall\theta\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{T}_{\mathrm{0}} ,{T}_{\mathrm{1}} {and}\:{T}_{\mathrm{2}} {and}\:{prove}\:{that}\: \\ $$$${T}_{{n}+\mathrm{2}} =\mathrm{2}{x}\:{T}_{{n}+\mathrm{1}} −{T}_{{n}}…
Question Number 73059 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{P}_{{n}} \left({x}\right)=\left({x}+\mathrm{1}\right)^{{n}} −\left({x}−\mathrm{1}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{fartorize}\:{inside}\:{C}\left({x}\right)\:{P}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\prod_{{k}=\mathrm{1}} ^{{p}} \:{cotan}\left(\frac{{k}\pi}{\mathrm{2}{p}+\mathrm{1}}\right) \\ $$ Commented by…
Question Number 73056 by mathmax by abdo last updated on 05/Nov/19 $${if}\:\left({xsina}+{cosa}\right)^{{n}} ={q}\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)+{r}\:{find}\:{r} \\ $$ Commented by mathmax by abdo last updated on 06/Nov/19…
Question Number 73055 by mathmax by abdo last updated on 05/Nov/19 $${decompose}\:{inside}\:{R}\left({x}\right)\:{the}\:{fraction}\:\:\frac{{x}^{\mathrm{4}} \:+{x}+\mathrm{1}}{{x}\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73057 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{P}_{{n}} =\left({x}+\mathrm{1}\right)^{\mathrm{2}{n}+\mathrm{1}} −{x}^{\mathrm{2}{n}+\mathrm{1}} −\mathrm{1} \\ $$$${prove}\:{that}\:{x}^{\mathrm{2}} \:+{x}\:{divide}\:\underset{{n}} {{P}} \\ $$ Answered by MJS last…
Question Number 73051 by mathmax by abdo last updated on 05/Nov/19 $${factorize}\:{inside}\:{R}\left[{X}\right] \\ $$$$\left.\mathrm{1}\right){X}^{\mathrm{5}} −\mathrm{1}\:\: \\ $$$$\left.\mathrm{2}\right){X}^{\mathrm{6}} \:+\mathrm{1} \\ $$ Commented by mathmax by abdo…