Question Number 17959 by tawa tawa last updated on 13/Jul/17 Answered by alex041103 last updated on 13/Jul/17 $${Because}\:{j}=\sqrt{−\mathrm{1}}={i}\:{we}\:{can}\:{use} \\ $$$${Euler}'{s}\:{formula} \\ $$$${e}^{{ix}} ={cos}\:{x}\:+\:{isin}\:{x} \\ $$$${z}={e}^{\mathrm{1}+{i}\frac{\pi}{\mathrm{2}}}…
Question Number 83293 by ~blr237~ last updated on 29/Feb/20 $${Let}\:\:{A}\begin{pmatrix}{−\mathrm{2}}\\{−\mathrm{1}}\end{pmatrix}\:\:,{B}\begin{pmatrix}{\mathrm{1}}\\{\mathrm{3}}\end{pmatrix}\:,\:{C}\begin{pmatrix}{−\mathrm{10}}\\{\:\mathrm{5}}\end{pmatrix}\:{three}\:{given}\:{points}\:{in}\:{the}\:{brand}\:\left({O},{I},{J}\right)\:{such}\:{as}\:{OI}={OJ}\:{and}\:\left({OI}\right)\bot\left({OJ}\right) \\ $$$$\:{D}\:{is}\:{a}\:{point}\:{such}\:{as}\:{AD}={AC}+\mathrm{2}\:\:{and}\:\:{CD}=\mathrm{2}\: \\ $$$${Prove}\:{correctly}\:{that}\:\:{BD}=\mathrm{13}\:.{Can}\:{you}\:{find}\:{the}\:{coordinate}\:{of}\:{D}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 83268 by M±th+et£s last updated on 29/Feb/20 Answered by mr W last updated on 29/Feb/20 Commented by mr W last updated on 29/Feb/20…
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}}. \\…