Question Number 1331 by a@b.c last updated on 23/Jul/15 $$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{different}\:\mathrm{complex}\:\mathrm{numbers} \\ $$$$\mathrm{with}\:\mid\beta\mid=\mathrm{1}\:\mathrm{then}\:\mid\frac{\beta−\alpha}{\mathrm{1}−\alpha\beta}\mid=? \\ $$ Commented by 123456 last updated on 23/Jul/15 $$\mid\alpha+\beta\mid\leqslant\mid\alpha\mid+\mid\beta\mid \\ $$$$\mid\beta−\alpha\mid\leqslant\mid\beta\mid+\mid\alpha\mid \\…
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Question Number 1239 by Rasheed Ahmad last updated on 17/Jul/15 $${Rasheed}\:{Ahmad}\:\left({Rasheed}\:{Soomro}\right) \\ $$$$\bullet\mathrm{For}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{where}\:\mathrm{x}\:\mathrm{and}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{both}\:{are} \\ $$$$\mathrm{real}\:\mathrm{the}\:\left(\mathrm{x},{f}\left({x}\right)\right)\:{can}\:{be}\:{plotted}\:{as} \\ $$$${a}\:{point}\:{easily}.\:\bullet{Now}\:{consider}\:{F}\left({X}\right) \\ $$$${where}\:{X}\:{and}\:{F}\left({X}\right)\:{are}\:{complex}\: \\ $$$${numbers}.\:{How}\:{can}\:\left({X},{F}\left({X}\right)\right)\:{be} \\ $$$${plotted}?\:{For}\:{a}\:{particular}\:{example}:\:\left(\mathrm{3}+\mathrm{2}{i},\mathrm{4}−\mathrm{5}{i}\right) \\ $$$${how}\:{can}\:{be}\:{plotted}?…
Question Number 66421 by Rio Michael last updated on 14/Aug/19 $${show}\:{that}\:{for}\:{a}\:{given}\:{complex}\:{number}\:{z} \\ $$$$\:{z}^{{n}} \:=\:{r}^{{n}} \:\left({cosn}\theta\:+\:{isinn}\theta\right)\: \\ $$ Answered by MJS last updated on 14/Aug/19 $${z}={r}\left(\mathrm{cos}\:\theta\:+\mathrm{i}\:\mathrm{sin}\:\theta\right)={r}\mathrm{e}^{\mathrm{i}\theta}…
Question Number 558 by 112358 last updated on 26/Jan/15 $${Determine}\:{the}\:{complex}\:{number} \\ $$$${z}\:{such}\:{that}\:{z}^{\mathrm{2}} ={tanx}+{icosx}, \\ $$$${in}\:{the}\:{form}\:{z}={p}+{ik},\:{p},{k}\in{R}. \\ $$$$ \\ $$ Answered by prakash jain last updated…
Question Number 226638 by Lara2440 last updated on 08/Dec/25 Commented by Lara2440 last updated on 08/Dec/25 $$\mathrm{Boy}'\mathrm{s}\:\mathrm{Surface}\:\mathrm{can}\:\mathrm{be}\:\mathrm{parametrized}\:\mathrm{in}\:\mathrm{several}\:\mathrm{ways} \\ $$$$\mathrm{Given}\:\mathrm{complex}\:\mathrm{number}\:{w}\:\mathrm{whose}\:\mid\mid{w}\mid\mid<\mathrm{1}, \\ $$$$\mathrm{Let}\:{g}_{\mu} =\begin{cases}{{g}_{\mathrm{1}} =−\frac{\mathrm{3}}{\mathrm{2}}\mathrm{Im}\left[\:\frac{{w}\left(\mathrm{1}−{w}^{\mathrm{4}} \right)}{{w}^{\mathrm{6}} +\sqrt{\mathrm{5}}{w}^{\mathrm{3}}…
Question Number 226372 by ajfour last updated on 26/Nov/25 Commented by ajfour last updated on 26/Nov/25 $${Find}\:{radii}\:\left({equal}\right)\:{of}\:{the}\:{two} \\ $$$${circles}.\:{Rectangle}\:{sides}\:{are} \\ $$$${length}\:{a}=\mathrm{2},\:{height}\:{b}=\mathrm{1}. \\ $$ Answered by…
Question Number 226124 by ajfour last updated on 20/Nov/25 Commented by ajfour last updated on 20/Nov/25 $${If}\:{s}=\mathrm{1},\:{find}\:{R}. \\ $$$${or}\:{find}\:{R}/{s}. \\ $$ Answered by fantastic2 last…
Question Number 225941 by mr W last updated on 16/Nov/25 Commented by mr W last updated on 16/Nov/25 $${Q}\mathrm{222520} \\ $$$${at}\:{least}\:{dropped}\:{from}\:{some}\:{points}, \\ $$$${the}\:{ball}\:{will}\:{return}\:{back}\:{to}\:{its} \\ $$$${starting}\:{position}\:{A}.…
Question Number 225604 by mr W last updated on 04/Nov/25 Commented by mr W last updated on 04/Nov/25 $${An}\:{uniform}\:{cylinder}\:{with}\:{radius}\:{R} \\ $$$${is}\:{spinned}\:{about}\:{its}\:{axis}\:{to}\:{the} \\ $$$${angular}\:{velocity}\:\omega_{\mathrm{0}} \:{and}\:{then}\:{placed} \\…
Question Number 224819 by Abdulazim last updated on 05/Oct/25 Answered by fantastic last updated on 05/Oct/25 Answered by Ghisom_ last updated on 06/Oct/25 $$\left(\mathrm{2}{x}^{\mathrm{3}} +{x}−{a}\right)^{\mathrm{3}}…