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Author: Tinku Tara

Question-201388

Question Number 201388 by MrGHK last updated on 05/Dec/23 Answered by witcher3 last updated on 05/Dec/23 $$=\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}}\underset{\mathrm{m}\geqslant\mathrm{0}} {\sum}\int_{\mathrm{0}} ^{\mathrm{1}} \left(−\mathrm{1}\right)^{\mathrm{m}} \mathrm{x}^{\mathrm{n}+\mathrm{2m}} \mathrm{dx} \\…

Question-201357

Question Number 201357 by sonukgindia last updated on 05/Dec/23 Commented by mahdipoor last updated on 05/Dec/23 $$\left(\mathrm{1}−\mathrm{4}{i}\right){z}=\mathrm{4}{ni}\Rightarrow{z}=\frac{\mathrm{4}{ni}}{\mathrm{1}−\mathrm{4}{i}}=\frac{\mathrm{4}{n}\left(\mathrm{4}+{i}\right)}{\mathrm{17}} \\ $$$${im}\left({z}\right)=\frac{\mathrm{4}{n}}{\mathrm{17}}=\mathrm{164}\Rightarrow{n}=\mathrm{17}×\mathrm{41}=\mathrm{697} \\ $$$${z}=\mathrm{656}+\mathrm{164}{i} \\ $$ Terms of…

2023-2023-mod-13-

Question Number 201352 by cortano12 last updated on 05/Dec/23 $$\:\:\:\mathrm{2023}^{\mathrm{2023}} \:=\:…\:\left(\mathrm{mod}\:\mathrm{13}\right) \\ $$ Answered by Rasheed.Sindhi last updated on 05/Dec/23 $$\:\:\:\mathrm{2023}^{\mathrm{2023}} \:\equiv\:…\:\left(\mathrm{mod}\:\mathrm{13}\right) \\ $$$$\mathrm{2023}^{\mathrm{2023}} \\…