Question Number 112746 by bemath last updated on 09/Sep/20 $$\mathrm{If}\:\mathrm{z}\:=\:−\mathrm{i}\:\mathrm{is}\:\mathrm{the}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{z}^{\mathrm{3}} +\mathrm{k}.\mathrm{z}^{\mathrm{2}} +\left(\mathrm{8}+\mathrm{2}\sqrt{\mathrm{2}}\:\mathrm{i}\right)\mathrm{z}+\mathrm{8i}\:=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{other}\:\mathrm{roots} \\ $$ Commented by malwan last updated on 09/Sep/20…
Question Number 112751 by bemath last updated on 09/Sep/20 Answered by bobhans last updated on 09/Sep/20 $$\mathrm{let}\:\mathrm{w}\:=\:\mathrm{a}+\mathrm{bi}\:\mathrm{and}\:\mathrm{z}\:=\:\mathrm{p}+\mathrm{qi}\: \\ $$$$\mathrm{where}\:\overset{−} {\mathrm{z}}=\mathrm{p}−\mathrm{qi}\: \\ $$$$\Rightarrow\mathrm{w}−\mathrm{2z}\:=\:\mathrm{a}+\mathrm{bi}−\mathrm{2p}−\mathrm{2qi}\:=\:\mathrm{9} \\ $$$$\Rightarrow\left(\mathrm{a}−\mathrm{2p}\right)+\left(\mathrm{b}−\mathrm{2q}\right)\mathrm{i}\:=\:\mathrm{9}+\mathrm{0}.\mathrm{i} \\…
Question Number 112737 by bemath last updated on 09/Sep/20 $$\mathrm{Given}\:\mathrm{z}=−\mathrm{6}+\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{i} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{two}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{z}^{\mathrm{n}} .\overset{−} {\mathrm{z}}\:\mathrm{purelly}\:\mathrm{imaginary}. \\ $$ Commented by bemath last updated on 09/Sep/20…
Question Number 112664 by bemath last updated on 09/Sep/20 $$\mathrm{what}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{parabola}\: \\ $$$$\mathrm{whose}\:\mathrm{focus}\:\mathrm{F}\left(−\mathrm{3},\mathrm{4}\right)\:\mathrm{and}\:\mathrm{directrix} \\ $$$$\mathrm{is}\:\mathrm{3x}−\mathrm{4y}+\mathrm{5}=\mathrm{0}\:? \\ $$ Commented by bemath last updated on 09/Sep/20 Answered by…
Question Number 112606 by ajfour last updated on 08/Sep/20 Commented by ajfour last updated on 10/Sep/20 $${Find}\:{minimum}\:{length}\:{of}\:{AE}\:{in} \\ $$$${terms}\:{of}\:{r},\:{a},\:{b}.\:\:\: \\ $$ Answered by mr W…
Question Number 178131 by cortano1 last updated on 13/Oct/22 Commented by Frix last updated on 13/Oct/22 $$\mathrm{the}\:\mathrm{radius}\:\mathrm{is}\:{s}×{r}\:\mathrm{with}\:{r}\:\mathrm{being}\:\mathrm{the}\:\mathrm{real} \\ $$$$\mathrm{solution}\:\mathrm{of} \\ $$$${r}^{\mathrm{3}} −\mathrm{2}{r}^{\mathrm{2}} +\frac{\mathrm{3}{r}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{0} \\ $$$$\mathrm{which}\:\mathrm{is}…
Question Number 112576 by ajfour last updated on 08/Sep/20 Commented by ajfour last updated on 08/Sep/20 $${Find}\:{OA}={AB}. \\ $$ Answered by mr W last updated…
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Question Number 46935 by ajfour last updated on 02/Nov/18 Commented by ajfour last updated on 03/Nov/18 $${If}\:{both}\:{coloured}\:{regions}\:{have}\:{the} \\ $$$${same}\:{area},\:{find}\:{locus}\:{of}\:{C}\:{in} \\ $$$${polar}\:{form}\:{or}\:{cartesian}\:{form}. \\ $$$${Take}\:{center}\:{of}\:{rectangle}\:{as}\:{origin}, \\ $$$${and}\:{radius}\:{of}\:{circle}\:{R}.…
Question Number 177980 by infinityaction last updated on 11/Oct/22 Answered by mr W last updated on 11/Oct/22 Commented by mr W last updated on 11/Oct/22…