Question Number 217101 by MathematicalUser2357 last updated on 01/Mar/25 $$\mathrm{is}\:\mathrm{this}\:\mathrm{right}\:\mathrm{when}\:\left({a}+{bi}\right)^{{c}+{di}} =\mid{a}+{bi}\mid^{{c}+{di}} {e}^{{i}\left({c}+{di}\right)\mathrm{arg}\left({a}+{bi}\right)} ? \\ $$$$\mathrm{I}\:\mathrm{had}\:\mathrm{let}\:\mathrm{arg}\left({a}+{bi}\right)=\begin{cases}{\mathrm{tan}^{−\mathrm{1}} \left(\frac{{b}}{{a}}\right)}&{{a}\geqslant\mathrm{0}\:\mathrm{and}\:{b}\geqslant\mathrm{0}}\\{\pi−\mathrm{tan}^{−\mathrm{1}} \left(−\frac{{b}}{{a}}\right)}&{{a}<\mathrm{0}\:\mathrm{and}\:{b}\geqslant\mathrm{0}}\\{−\left(\pi−\mathrm{tan}^{−\mathrm{1}} \left(\frac{{b}}{{a}}\right)\right)}&{{a}<\mathrm{0}\:\mathrm{and}\:{b}<\mathrm{0}}\\{−\mathrm{tan}^{−\mathrm{1}} \left(\frac{{b}}{{a}}\right)}&{{a}\geqslant\mathrm{0}\:\mathrm{and}\:{b}<\mathrm{0}}\end{cases}\:\mathrm{before}\:\mathrm{I}\:\mathrm{solved}\:\mathrm{it} \\ $$$$\left({a}+{bi}\right)^{{c}+{di}} =\mid{a}+{bi}\mid^{{c}+{di}} {e}^{{i}\left({c}+{di}\right)\mathrm{arg}\left({a}+{bi}\right)} \\ $$$$=\mid{a}+{bi}\mid^{{c}}…
Question Number 217121 by Engr_Jidda last updated on 01/Mar/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 217122 by efronzo1 last updated on 01/Mar/25 $$\:\:\:\:\:\int\:\frac{\sqrt{\mathrm{cos}\:\mathrm{2x}}}{\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by Frix last updated on 01/Mar/25 $$\int\frac{\sqrt{\mathrm{cos}\:\mathrm{2}{x}}}{\mathrm{cos}\:{x}}{dx}=\int\frac{\sqrt{−\mathrm{1}+\mathrm{2cos}^{\mathrm{2}} \:{x}}}{\mathrm{cos}\:{x}}{dx}\:\overset{\left[{t}=\sqrt{\mathrm{2}}\mathrm{sin}\:{x}\right]} {=} \\ $$$$=\sqrt{\mathrm{2}}\int\frac{\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{\mathrm{2}−{t}^{\mathrm{2}}…
Question Number 217084 by maths_plus last updated on 28/Feb/25 $$\boldsymbol{\mathrm{Geometr}}\mathrm{i}\boldsymbol{\mathrm{e}}\:\boldsymbol{\mathrm{dans}}\:\boldsymbol{\mathrm{le}}\:\boldsymbol{\mathrm{plan}}. \\ $$$$\overset{\rightarrow} {\mathrm{AB}}\:\mathrm{et}\:\overset{\rightarrow} {\mathrm{CD}}\:\mathrm{sont}\:\mathrm{deux}\:\mathrm{vecteurs}\:\mathrm{du}\:\mathrm{plan}. \\ $$$$\overset{\rightarrow} {\mathrm{AB}}\:\mathrm{n}'\mathrm{est}\:\mathrm{pas}\:\mathrm{nul}. \\ $$$$\mathrm{Demontre}\:\mathrm{que}\:\mathrm{si}\:\overset{\rightarrow} {\mathrm{AB}}\:\mathrm{et}\:\overset{\rightarrow} {\mathrm{CD}}\:\mathrm{sont}\:\mathrm{colineaires} \\ $$$$\mathrm{alors}\:\mathrm{il}\:\mathrm{existe}\:\mathrm{un}\:\mathrm{nombre}\:\mathrm{reel}\:\mathrm{k}\:\mathrm{tel}\:\mathrm{que} \\ $$$$\overset{\rightarrow}…
Question Number 217085 by mat2727 last updated on 28/Feb/25 Commented by mr W last updated on 01/Mar/25 $${i}\:{think}\:{there}\:{is}\:{no}\:{unique}\:{solution}. \\ $$$$\mathrm{0}<{x}\leqslant\mathrm{12} \\ $$ Commented by mr…
Question Number 217080 by hardmath last updated on 28/Feb/25 Commented by mr W last updated on 01/Mar/25 $${also}\:{Area}\left({ABCD}\right)\leqslant\sqrt{{abcd}} \\ $$ Answered by mr W last…
Question Number 217079 by idos last updated on 28/Feb/25 $$\frac{\mathrm{6}{C}\mathrm{3}×\mathrm{4}{C}\mathrm{1}}{\mathrm{15}{C}\mathrm{4}} \\ $$$$ \\ $$ Answered by MrGaster last updated on 01/Mar/25 $$=\frac{\mathrm{6}×\mathrm{4}}{\mathrm{1365}} \\ $$$$=\frac{\mathrm{24}}{\mathrm{1365}} \\…
Question Number 217075 by maths_plus last updated on 28/Feb/25 $$ \\ $$Help me please… $\vv{AB}$ and $\vv{CD}$ are two vectors, and $\vv{AB}$ is not the…
Question Number 217068 by yusif last updated on 28/Feb/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 217071 by ArshadS last updated on 28/Feb/25 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{two}-\mathrm{digit}\:\mathrm{numbers}\:\mathrm{that}\:\mathrm{are}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{four}\:\mathrm{times}\:\mathrm{the}\:\mathrm{sum}\: \\ $$$$\mathrm{of}\:\mathrm{their}\:\mathrm{digits}.\:\mathrm{Solve}\:\mathrm{this}\:\mathrm{using}\:\mathrm{at}\:\mathrm{least}\:\mathrm{two}\:\mathrm{different}\:\mathrm{methods}\: \\ $$$$\mathrm{and}\:\mathrm{verify}\:\mathrm{your}\:\mathrm{answers}. \\ $$ Answered by som(math1967) last updated on 28/Feb/25 $$\:{x}+\mathrm{10}{y}=\mathrm{4}\left({x}+{y}\right) \\…