Question Number 102581 by bemath last updated on 10/Jul/20
$${If}\:{x}+{iy}\:=\:\mathrm{3}+\mathrm{2}{xi}\: \\ $$$$.\:{find}\:{y} \\ $$
Answered by bemath last updated on 10/Jul/20
Answered by Rasheed.Sindhi last updated on 10/Jul/20
$$\:\:\:{x}+{iy}\:=\:\mathrm{3}+\mathrm{2}{xi}\: \\ $$$$\:\:\:\:{x}=\mathrm{3}\:\wedge\:{y}=\mathrm{2}{x} \\ $$$$\:\:\:\:{y}=\mathrm{2}{x}=\mathrm{2}\left(\mathrm{3}\right)=\mathrm{6}\:\:\:\:\underset{\smile} {\overset{\frown} {\bullet}}\:\overset{\frown} {\bullet} \\ $$
Commented by bemath last updated on 10/Jul/20
$$\overset{\frown\:\bullet\:\frown} {\smile} \\ $$
Commented by 1549442205 last updated on 10/Jul/20
$$\mathrm{if}\:\mathrm{given}\:\mathrm{x},\mathrm{y}\:\mathrm{are}\:\mathrm{real}\:\mathrm{then}\:\mathrm{the}\:\mathrm{case}\:\mathrm{x}^{\mathrm{2}} =\frac{−\mathrm{9}}{\mathrm{4}} \\ $$$$\mathrm{need}\:\mathrm{rejected}\:\mathrm{and}\:\mathrm{y}=\mathrm{6}\:\mathrm{is}\:\mathrm{unique}\:\mathrm{root} \\ $$
Commented by bemath last updated on 10/Jul/20
$${yes}...{agree} \\ $$
Answered by Dwaipayan Shikari last updated on 10/Jul/20
$${x}+{iy}=\mathrm{3}+\mathrm{2}{xi} \\ $$$${y}=\mathrm{2}{x}\:\:\:{x}=\mathrm{3} \\ $$$${so}\:{y}=\mathrm{2}.\mathrm{3}=\mathrm{6}\:\:\:\:\:\:\:\:\:\ddots\iddots\ddots\iddots\ddots\iddots\vdots\ldots\vdots\ldots\vdots\ldots \\ $$
Answered by mathmax by abdo last updated on 10/Jul/20
$$\left(\mathrm{1},\mathrm{i}\right)\mathrm{is}\:\mathrm{a}\:\mathrm{base}\:\mathrm{so}\:\mathrm{x}+\mathrm{iy}\:=\mathrm{3}\:+\mathrm{2xi}\:\Rightarrow\mathrm{x}=\mathrm{3}\:\mathrm{and}\:\mathrm{y}\:=\mathrm{2x}\:\Rightarrow\mathrm{x}=\mathrm{3}\:\mathrm{and}\:\mathrm{y}\:=\mathrm{6} \\ $$