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Category: Algebra

Why-arg-z-arg-z-2kpi-k-Z-Shouldn-t-it-be-always-0-

Question Number 19250 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Why}\:\mathrm{arg}\left({z}\right)\:+\:\mathrm{arg}\left(\bar {{z}}\right)\:=\:\mathrm{2}{k}\pi,\:{k}\:\in\:{Z}? \\ $$$$\mathrm{Shouldn}'\mathrm{t}\:\mathrm{it}\:\mathrm{be}\:\boldsymbol{\mathrm{always}}\:\mathrm{0}? \\ $$ Commented by ajfour last updated on 07/Aug/17 $$\mathrm{yes},\:\mathrm{so}\:\mathrm{do}\:\mathrm{i}\:\mathrm{think}. \\ $$$$\mathrm{but}\:\mathrm{if}\:{z}=−\mathrm{1}\:?!…

Find-ax-5-by-5-if-the-real-numbers-a-b-x-and-y-satisf-the-equations-ax-by-3-ax-2-by-2-7-ax-3-by-3-16-ax-4-by-4-42-

Question Number 150326 by mathdanisur last updated on 11/Aug/21 $$\mathrm{Find}\:\:\boldsymbol{\mathrm{ax}}^{\mathrm{5}} +\boldsymbol{\mathrm{by}}^{\mathrm{5}} \:\:\mathrm{if}\:\mathrm{the}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{satisf}\:\mathrm{the}\:\mathrm{equations}: \\ $$$$\mathrm{ax}\:+\:\mathrm{by}\:=\:\mathrm{3} \\ $$$$\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{by}^{\mathrm{2}} \:=\:\mathrm{7} \\ $$$$\mathrm{ax}^{\mathrm{3}} \:+\:\mathrm{by}^{\mathrm{3}} \:=\:\mathrm{16} \\…

at-what-time-is-the-short-clock-and-long-hour-hand-form-an-angle-of-180-degrees-

Question Number 84785 by john santu last updated on 16/Mar/20 $$\mathrm{at}\:\mathrm{what}\:\mathrm{time}\:\mathrm{is}\:\mathrm{the}\:\mathrm{short}\:\mathrm{clock}\: \\ $$$$\mathrm{and}\:\mathrm{long}\:\mathrm{hour}\:\mathrm{hand}\:\mathrm{form}\:\mathrm{an}\: \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{180}\:\mathrm{degrees}? \\ $$ Commented by mr W last updated on 16/Mar/20…

Let-f-x-be-a-quadratic-polynomial-with-integer-coefficients-such-that-f-0-and-f-1-are-odd-integers-Prove-that-the-equation-f-x-0-does-not-have-an-integer-solution-

Question Number 19245 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Let}\:{f}\left({x}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{polynomial} \\ $$$$\mathrm{with}\:\mathrm{integer}\:\mathrm{coefficients}\:\mathrm{such}\:\mathrm{that}\:{f}\left(\mathrm{0}\right) \\ $$$$\mathrm{and}\:{f}\left(\mathrm{1}\right)\:\mathrm{are}\:\mathrm{odd}\:\mathrm{integers}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{equation}\:{f}\left({x}\right)\:=\:\mathrm{0}\:\mathrm{does}\:\mathrm{not}\:\mathrm{have}\:\mathrm{an} \\ $$$$\mathrm{integer}\:\mathrm{solution}. \\ $$ Commented by RasheedSindhi last updated…

Question-19236

Question Number 19236 by chernoaguero@gmail.com last updated on 07/Aug/17 Answered by ,25>( last updated on 07/Aug/17 $${x}\:=\:\mathrm{2}\:\mathrm{since}\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:=\:\mathrm{13}. \\ $$ Commented by chernoaguero@gmail.com last…