Question Number 73113 by TawaTawa last updated on 06/Nov/19 Commented by mathmax by abdo last updated on 06/Nov/19 $$\left.\mathrm{1}\right)\:{we}\:{have}\:{arg}\left({z}\right)={arg}\left(\mathrm{7}−\mathrm{3}\sqrt{\mathrm{3}}{i}\right)+{arg}\left(−\mathrm{1}−{i}\right)\left[\mathrm{2}\pi\right] \\ $$$$\mid\mathrm{7}−\mathrm{3}\sqrt{\mathrm{3}}\mid\:=\sqrt{\mathrm{49}+\mathrm{27}}=\sqrt{\mathrm{76}}\:\Rightarrow\mathrm{7}−\mathrm{3}\sqrt{\mathrm{3}}=\sqrt{\mathrm{76}}{e}^{{iarctan}\left(\frac{−\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{7}}\right)} \:\Rightarrow \\ $$$${arg}\left(\mathrm{7}−\mathrm{3}\sqrt{\mathrm{3}}\right)\:=−{arctan}\left(\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{7}}\right) \\…
Question Number 7577 by Tawakalitu. last updated on 04/Sep/16 $${p}\:=\:\frac{{a}\left[\mathrm{1}\:−\:\left(\mathrm{1}\:+\:{r}\right)^{−{n}} \right]}{{r}} \\ $$$$ \\ $$$${Make}\:\:\:{r}\:\:\:{the}\:{subject}\:{of}\:{the}\:{fomular}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138641 by soudo last updated on 15/Apr/21 Answered by MJS_new last updated on 16/Apr/21 $$\left.\mathrm{f}\left.\mathrm{rom}\:\mathrm{1}\right)\:\Rightarrow\:\mathrm{2}\right) \\ $$$${x}^{\mathrm{2}} \pm{xy}+{y}^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{2}}\left({x}^{\mathrm{2}} +{x}^{\mathrm{2}} \pm\mathrm{2}{xy}+{y}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)=…
Question Number 7532 by Yozzia last updated on 02/Sep/16 $${Find}\:{x}_{{n}} \:\left({n}\in\mathbb{Z}\right)\:{satisfying}\:{x}_{\mathrm{0}} =\mathrm{0},\:{x}_{\mathrm{1}} =\mathrm{1}\:{and} \\ $$$${x}_{{n}+\mathrm{1}} ={x}_{{n}} \sqrt{{x}_{{n}−\mathrm{1}} ^{\mathrm{2}} +\mathrm{1}}+{x}_{{n}−\mathrm{1}} \sqrt{{x}_{{n}} ^{\mathrm{2}} +\mathrm{1}}\:{for}\:{n}\geqslant\mathrm{1}. \\ $$ Commented…
Question Number 73042 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:{for}\:\left({n},{p}\right)\in{N}^{\bigstar^{\mathrm{2}} } \:\:\:\sum_{{k}=\mathrm{0}} ^{{p}\:} \:{k}\:{C}_{{n}} ^{{p}−{k}} \:{C}_{{n}} ^{{k}} \:={n}\:{C}_{\mathrm{2}{n}−\mathrm{1}} ^{{p}−\mathrm{1}} \\ $$$${conclude}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}\:\left({C}_{{n}}…
Question Number 73041 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\forall{n}\in\:{N}\:\:\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}} \:\left(−\mathrm{1}\right)^{{k}} \:\left({C}_{\mathrm{2}{n}} ^{{k}} \right)^{\mathrm{2}} \:=\left(−\mathrm{1}\right)^{{n}} \:{C}_{\mathrm{2}{n}} ^{{n}} \\ $$ Commented by mathmax…
Question Number 73040 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\:\forall\left({n},{p}\right)\in{N}^{\bigstar} ×{N} \\ $$$$\left.\mathrm{1}\right)\sum_{{k}=\mathrm{0}} ^{{p}} \:\left(−\mathrm{1}\right)^{{k}} \:{C}_{{n}} ^{{k}} \:=\left(−\mathrm{1}\right)^{{p}} \:{C}_{{n}−\mathrm{1}} ^{{p}} \\ $$$$\left.\mathrm{2}\right)\forall\left({p},{q}\right)\in{N}^{\mathrm{2}} \:\:\:\:\sum_{{k}=\mathrm{0}}…
Question Number 73039 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{U}_{{n}} =\frac{{n}}{\mathrm{2}}\:{if}\:{n}\:{even}\:{and}\:{U}_{{n}} =\frac{{n}−\mathrm{1}}{\mathrm{2}}\:{if}\:{n}\:{odd}\:{let}\:{f}\left({n}\right)=\sum_{{k}=\mathrm{0}} ^{{n}} {U}_{{k}} \\ $$$${prove}\:{that}\:\forall\left({x},{y}\right)\in{N}^{\mathrm{2}} \:\:\:\:{f}\left({x}+{y}\right)−{f}\left({x}−{y}\right)={xy} \\ $$ Answered by mind is…
Question Number 73036 by mathmax by abdo last updated on 05/Nov/19 $$\left.{calculate}\:\mathrm{1}\right)\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{k}^{\mathrm{2}} \left({n}+\mathrm{1}−{k}\right) \\ $$$$\left.\mathrm{2}\right)\sum_{\mathrm{1}\leqslant{i}\leqslant{j}\leqslant{n}} \:{ij} \\ $$ Commented by mathmax by abdo…
Question Number 7500 by Tawakalitu. last updated on 31/Aug/16 $$\mathrm{5}^{\sqrt{{x}\:}} \:−\:\:\mathrm{5}^{{x}\:−\:\mathrm{7}} \:\:=\:\:\mathrm{100} \\ $$$$ \\ $$$${Find}\:{the}\:{value}\:{of}\:{x}. \\ $$$${x}\:=\:\mathrm{9}\:\:\:{please}\:{workings}. \\ $$ Answered by sandy_suhendra last updated…