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Category: Operation Research

donner-la-forme-trigonometrique-de-1-i-3-1-i-cos-isin-

Question Number 176366 by doline last updated on 17/Sep/22 $${donner}\:{la}\:{forme}\:{trigonometrique}\:{de}\left(\mathrm{1}−{i}\sqrt{}\mathrm{3}\right)\left(\mathrm{1}+{i}\right)\left({cos}\theta−{isin}\theta\right) \\ $$ Answered by Ar Brandon last updated on 17/Sep/22 $$\left(\mathrm{2}{e}^{−\frac{\pi}{\mathrm{3}}{i}} \right)\left(\sqrt{\mathrm{2}}{e}^{\frac{\pi}{\mathrm{4}}{i}} \right)\left({e}^{−{i}\theta} \right)=\mathrm{2}\sqrt{\mathrm{2}}{e}^{\left(−\frac{\pi}{\mathrm{3}}+\frac{\pi}{\mathrm{4}}−\theta\right){i}} \\…

demontrer-par-recurrence-que-pour-tout-n-gt-0-appartenent-a-l-ensemble-des-entier-naturel-3-2n-2-n-est-multiple-de-7-

Question Number 176070 by doline last updated on 11/Sep/22 $${demontrer}\:{par}\:{recurrence}\:{que}\:{pour}\:{tout}\:{n}>\mathrm{0}\:{appartenent}\:{a}\:{l}\:{ensemble}\:{des}\:{entier}\:{naturel}\:\mathrm{3}^{\mathrm{2}{n}−\mathrm{2}^{{n}\:} } {est}\:{multiple}\:{de}\:\mathrm{7} \\ $$ Commented by som(math1967) last updated on 11/Sep/22 $$\mathrm{3}^{\mathrm{2}{n}} −\mathrm{2}^{{n}} \\ $$$${p}\left(\mathrm{1}\right)=\mathrm{3}^{\mathrm{2}}…

x-2-4x-5-0-

Question Number 176060 by doline last updated on 11/Sep/22 $${x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}=\mathrm{0} \\ $$ Answered by Ar Brandon last updated on 11/Sep/22 $${x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}=\mathrm{0}\:\Rightarrow\left({x}−\mathrm{2}\right)^{\mathrm{2}} +\mathrm{1}=\mathrm{0} \\…

calculer-1-2-i-3-2-3-

Question Number 176049 by doline last updated on 11/Sep/22 $${calculer}\:\left(−\mathrm{1}/\mathrm{2}+{i}\sqrt{\left.\mathrm{3}/\mathrm{2}\right)^{\mathrm{3}} }\right. \\ $$ Answered by Rasheed.Sindhi last updated on 11/Sep/22 $$−\mathrm{1}/\mathrm{2}+{i}\sqrt{\left.\mathrm{3}/\mathrm{2}\right)^{\mathrm{3}} } \\ $$$$=−\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{i}\left(\sqrt{\mathrm{3}/\mathrm{2}}\:\right)^{\mathrm{3}} \\…