Question Number 17393 by tawa tawa last updated on 05/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{modulus}\:\mathrm{of}\:\:\mathrm{z}\:=\:\mathrm{6}\:+\:\mathrm{8i} \\ $$ Answered by ajfour last updated on 05/Jul/17 $$\mid\mathrm{z}\mid=\sqrt{\left(\mathrm{6}\right)^{\mathrm{2}} +\left(\mathrm{8}\right)^{\mathrm{2}} }\:=\mathrm{10}\:. \\ $$…
Question Number 17391 by tawa tawa last updated on 05/Jul/17 $$\mathrm{write}\:\:\:\mathrm{z}\:=\:\left(\mathrm{2}\:+\:\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{i}\right)^{\mathrm{3}} \:\:\mathrm{in}\:\mathrm{polar}\:\mathrm{form}. \\ $$ Answered by ajfour last updated on 05/Jul/17 $$\mathrm{z}=\mathrm{4}^{\mathrm{3}} \left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{i}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{3}} =\mathrm{64}\left(\mathrm{e}^{\boldsymbol{\mathrm{i}}\pi/\mathrm{3}} \right)^{\mathrm{3}}…
Question Number 17302 by ajfour last updated on 03/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\: \\ $$$$\:\:\rho=\mathrm{a}\left(\mathrm{1}−\mathrm{cos}\:\theta\right)\:. \\ $$$$\:\rho=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\:,\:\:\theta=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{y}}{\mathrm{x}}\right)\:. \\ $$ Commented by ajfour last updated on…
Question Number 148151 by puissant last updated on 25/Jul/21 Answered by Olaf_Thorendsen last updated on 25/Jul/21 $$\mathrm{1}. \\ $$$$\left({u}_{{n}} \right)_{{n}\in\mathbb{N}^{\ast} } \:\mathrm{est}\:\mathrm{de}\:\mathrm{type}\:\mathcal{M}. \\ $$$$\mathrm{Donc}\:\forall{n}\in\mathbb{N}^{\ast} ,\:{u}_{{n}}…
Question Number 16917 by tawa tawa last updated on 28/Jun/17 $$\mathrm{If}\:\:\:\mathrm{x}\:+\:\mathrm{iy}\:=\:\frac{\mathrm{1}}{\mathrm{a}\:+\:\mathrm{ib}} \\ $$$$\mathrm{prove}\:\mathrm{that}\::\:\:\:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \right)\:=\:\mathrm{1} \\ $$ Answered by Tinkutara last updated on…
Question Number 16857 by tawa tawa last updated on 27/Jun/17 $$\mathrm{Suppose}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{are}\:\mathrm{vectors}\:\mathrm{in}\:\mathbb{R}^{\mathrm{n}} \:\mathrm{that}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{length}.\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:\:\mathrm{bisect}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}. \\ $$ Answered by 1234Hello last updated on 06/Jul/17 $$\mathrm{It}\:\mathrm{is}\:\mathrm{just}\:\mathrm{like}\:\mathrm{vectors}\:\boldsymbol{\mathrm{i}}\:\mathrm{and}\:\boldsymbol{\mathrm{j}}. \\…
Question Number 16748 by Tinkutara last updated on 26/Jun/17 $$\mathrm{Let}\:{H}\:\mathrm{be}\:\mathrm{orthocenter}\:\mathrm{of}\:\Delta{ABC}\:\mathrm{and}\:{O} \\ $$$$\mathrm{its}\:\mathrm{circumcenter}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{vectors} \\ $$$$\overset{\rightarrow} {{OA}},\:\overset{\rightarrow} {{OB}},\:\overset{\rightarrow} {{OC}}\:\mathrm{and}\:\overset{\rightarrow} {{OH}}\:\mathrm{satisfy}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{equality}: \\ $$$$\overset{\rightarrow} {{OA}}\:+\:\overset{\rightarrow} {{OB}}\:+\:\overset{\rightarrow} {{OC}}\:=\:\overset{\rightarrow}…
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Question Number 82277 by M±th+et£s last updated on 19/Feb/20 Commented by M±th+et£s last updated on 19/Feb/20 $${find}\:{the}\:{area}\:{of}\:\:{the}\:{rectangle} \\ $$ Commented by mr W last updated…
Question Number 16656 by Tinkutara last updated on 24/Jun/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{with}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{10} \\ $$$$\mathrm{ms}^{−\mathrm{1}} \:\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},\:−\mathrm{2}\right)\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{direction}\:\mathrm{3}\overset{\wedge} {{i}}\:+\:\mathrm{4}\overset{\wedge} {{j}}.\:\mathrm{The}\:\mathrm{position}\:\mathrm{vector} \\ $$$$\mathrm{after}\:\mathrm{3}\:\mathrm{s}\:\mathrm{is} \\ $$ Answered by sma3l2996 last…