Question Number 226581 by klipto last updated on 06/Dec/25 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{polar}}\:\boldsymbol{\mathrm{of}} \\ $$$$\left(\mathrm{1}+\boldsymbol{\mathrm{i}}\right)\left(\mathrm{1}+\boldsymbol{\mathrm{i}}\sqrt{\mathrm{3}}\right) \\ $$ Answered by Frix last updated on 06/Dec/25 $$=\sqrt{\mathrm{2}}\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{4}}} ×\mathrm{2e}^{\mathrm{i}\frac{\pi}{\mathrm{3}}} =\mathrm{2}\sqrt{\mathrm{2}}\mathrm{e}^{\mathrm{i}\frac{\mathrm{7}\pi}{\mathrm{12}}} \\…
Question Number 226577 by mr W last updated on 06/Dec/25 Answered by Ghisom_ last updated on 06/Dec/25 $${x}_{\mathrm{1}} =\alpha+\sqrt{\beta}+\sqrt{\gamma}+\sqrt{\beta\gamma} \\ $$$${x}_{\mathrm{2}} =\alpha−\sqrt{\beta}−\sqrt{\gamma}+\sqrt{\beta\gamma} \\ $$$${x}_{\mathrm{3}} =\alpha−\sqrt{\beta}+\sqrt{\gamma}−\sqrt{\beta\gamma}…
Question Number 226573 by Lara2440 last updated on 06/Dec/25 $$\mathrm{Parametric}\:\mathrm{Surface}\:\hat {\boldsymbol{\mathrm{r}}}\left({u},{v}\right);\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R}^{\mathrm{3}} \\ $$$$\hat {\boldsymbol{\mathrm{r}}}\left({u},{v}\right)=\begin{cases}{{a}\centerdot\mathrm{sin}\left({u}\right)\mathrm{cos}\left({v}\right)}\\{{a}\centerdot\mathrm{sin}\left({u}\right)\mathrm{sin}\left({v}\right)}\\{{a}\centerdot\mathrm{cos}\left({u}\right)}\end{cases}\:\:\:{a}>\mathrm{0}\:,\:\mathrm{0}\leq{u}\leq\pi\:,\:\mathrm{0}\leq{v}\leq\mathrm{2}\pi \\ $$$$\mathrm{1}.\:\mathrm{Find}\:\mathrm{Principal}\:\mathrm{Direction} \\ $$$$\mathrm{2}.\:\mathrm{Find}\:\mathrm{Principal}\:\mathrm{Curvature} \\ $$$$\mathrm{3}.\:\mathrm{Find}\:\mathrm{Gauss}\:\mathrm{Curvature} \\ $$$$\mathrm{4}.\:\mathrm{Find}\:\mathrm{Euler}\:\mathrm{Characteristic}\: \\ $$$$\mathrm{Hint}\:…
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Question Number 226593 by Mingma last updated on 06/Dec/25 Commented by fantastic2 last updated on 07/Dec/25 $${option}\:{B} \\ $$ Commented by fantastic2 last updated on…
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Question Number 226572 by mr W last updated on 05/Dec/25 Answered by mr W last updated on 07/Dec/25 Commented by mr W last updated on…
Question Number 226569 by hardmath last updated on 05/Dec/25 $$\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \:=\:\mathrm{2d}^{\mathrm{2}} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{an}\:\mathrm{infinite} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{solutions} \\ $$ Commented by mr W last updated…
Question Number 226558 by hardmath last updated on 04/Dec/25 Answered by mr W last updated on 04/Dec/25 Commented by hardmath last updated on 05/Dec/25 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{my}\:\mathrm{dear}\:\mathrm{professor}\:\mathrm{cool}…