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Question Number 104333 by 175mohamed last updated on 20/Jul/20 $${if}\:{i}^{\:\mathrm{5}{n}\:+\mathrm{1}\:} =\:\mathrm{1}\:\:\:\:,\:{n}\in{Z} \\ $$$${then}\:{show}\:{that}\::\:{n}\:=\:\mathrm{3}+\mathrm{4}{p}\:\:\:,{p}\in{Z} \\ $$ Answered by OlafThorendsen last updated on 20/Jul/20 $${i}^{\mathrm{5}{n}+\mathrm{1}} \:=\:\mathrm{1}\:=\:{i}^{\mathrm{4}{k}} \\…
Question Number 169836 by Mastermind last updated on 10/May/22 Answered by Nunzio last updated on 10/May/22 $$ \\ $$$${y}=\mid{x}^{\mid{x}\mid} \mid\:\:\:\:\:\:\:\:\:{D}:{x}>\mathrm{0}\:\Rightarrow\mid{x}^{\mid{x}\mid} \mid={x}^{{x}} \\ $$$$ \\ $$$${y}={x}^{{x}}…
Question Number 104296 by Dwaipayan Shikari last updated on 20/Jul/20 $$ \\ $$$$ \\ $$$$\mathrm{FUN}\:\mathrm{TIME}\:\mathrm{AGAIN}! \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+.. \\…
Question Number 169812 by Mastermind last updated on 09/May/22 $${Show}\:{that}\:{f}\left({z}\right)={z}^{\mathrm{2}} \:{is}\:{harmonic}\:{in}\:{the} \\ $$$${polar}\:{form} \\ $$$$ \\ $$$${Mastermind} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 169808 by Mastermind last updated on 09/May/22 $${If}\:{the}\:{Real}\:{component}\:{of}\:{an}\:{analytic} \\ $$$${function}\:{is}\:{given}\:{by}\:{log}_{{e}} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} , \\ $$$${find}\:{the}\:{function}. \\ $$$$ \\ $$$${Mastermind} \\ $$ Terms…
Question Number 169811 by Mastermind last updated on 09/May/22 $${Show}\:{that}\:{f}\left({z}\right)={z}\:{is}\:{harmonic}\:{in}\:{the} \\ $$$${polar}\:{form} \\ $$$$ \\ $$$${Mastermind} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 169807 by Mastermind last updated on 09/May/22 $${Given}\:{that}\:{U}={x}^{\mathrm{4}} −\mathrm{6}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +{y}^{\mathrm{4}} ,\:{find} \\ $$$${v}\:{and}\:{w}\:{such}\:{that}\:{w}={u}+{iv}\:{is}\:{analytic} \\ $$$$ \\ $$$${Mastermind} \\ $$ Terms of Service…
Question Number 38734 by Rio Mike last updated on 28/Jun/18 $${Find}\:{the}\:{domain}\:{of}\:{the}\:{function} \\ $$$${f}\:\left({x}\right)\:=\:\mathrm{1}\:−\:{cos}^{\mathrm{2}} \:{x} \\ $$ Commented by MrW3 last updated on 29/Jun/18 $${x}\in\left(−\infty,+\infty\right) \\…