Question Number 221697 by fantastic last updated on 09/Jun/25 $${Is}\:\sqrt{{i}}\:{an}\:{imaginary}\:{number}\:\left({i}=\sqrt{−\mathrm{1}}\right)\:{answer}\:{with}\:{logic} \\ $$ Answered by Ghisom last updated on 09/Jun/25 $$\mathrm{i}=\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{2}}} \\ $$$${z}={r}\mathrm{e}^{\mathrm{i}\theta} \:\Rightarrow\:\sqrt{{z}}=\sqrt{{r}}\mathrm{e}^{\mathrm{i}\frac{\theta}{\mathrm{2}}} \\ $$$$\Rightarrow\:\sqrt{\mathrm{i}}=\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{4}}}…
Question Number 221620 by fantastic last updated on 08/Jun/25 $${Solve}\:{for}\:{x} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{7}{x}}=\sqrt{{x}}\left[{x}\neq\mathrm{0}\right] \\ $$ Answered by fantastic last updated on 08/Jun/25 $${or}\:\left(\mathrm{7}{x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} ={x}^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$${or}\:\sqrt[{\mathrm{3}}]{\mathrm{7}}.{x}^{\frac{\mathrm{1}}{\mathrm{3}}}…
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Question Number 221498 by wewji12 last updated on 07/Jun/25 $$\mathrm{Solve}\:\mathrm{differantial}\:\mathrm{Equation} \\ $$$$\frac{{d}\:\:}{{dt}}\left[\frac{{dy}\left({t}\right)}{{dt}}\right]+{ty}\left({t}\right)=\mathrm{0} \\ $$ Answered by MrGaster last updated on 07/Jun/25 $${y}\left({t}\right)={C}_{\mathrm{1}} \underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{m}}…
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Question Number 221470 by wewji12 last updated on 06/Jun/25 Answered by MathematicalUser2357 last updated on 06/Jun/25 $$\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221481 by MrGaster last updated on 06/Jun/25 $$\mathrm{prove}:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{{k}!\left({n}−{k}\right)!}{{n}!}=−\frac{{i}\mathrm{2}^{{n}−\mathrm{1}} \Gamma\left({n}+\mathrm{2}\right)\left(\pi−{iB}_{\mathrm{2}} \left({n}+\mathrm{2},\mathrm{0}\right)\right)}{{n}!} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221473 by wewji12 last updated on 06/Jun/25 Answered by MathematicalUser2357 last updated on 06/Jun/25 $$\mathrm{279}\pi \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221435 by wewji12 last updated on 05/Jun/25 $$\mathrm{g};\mathbb{R}\rightarrow\mathbb{R}\:,\:\mathrm{g}\in\mathcal{C}^{\omega} \:\mathrm{at}\:\mathbb{R}\:\mathrm{space} \\ $$$$\:\mathrm{evauate}\: \\ $$$$−\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \:{y}\centerdot\mathrm{g}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\mathrm{d}{x}\mathrm{d}{y} \\ $$$$\mathrm{when}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{z}^{\mathrm{2}}…
Question Number 221447 by Nicholas666 last updated on 05/Jun/25 $$ \\ $$$$\:\:\:\:\mathrm{if}\:\:\:\:\:\:\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\:\left({x}\:+\:{r}_{{i}} \right)\:\equiv\:\underset{{j}=\mathrm{0}} {\overset{{n}} {\sum}}\:{a}_{{j}} {x}^{{n}−{i}} \: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\:; \\ $$$$\:\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{tan}^{−\mathrm{1}}…