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Question Number 38044 by solihin last updated on 21/Jun/18

Commented by math khazana by abdo last updated on 22/Jun/18

$$z\stackrel{-}{z}=5and\frac{z}{\stackrel{-}{z}}=-1+\frac{12}{5}i\Rightarrow \mid z^{}{\mid }^2=5\Rightarrow \mid z\mid =\sqrt{5}$$$$\frac{z}{\stackrel{-}{z}}=\frac{z^2}{z\stackrel{-}{z}}=\frac{z^2}{5}=-1+\frac{12}{5}i\Rightarrow z^2=-5+12i$$$$\mid -5+12i\mid =\sqrt{25+144}=\sqrt{169}=13\ne \mid z{\mid }^2=5so$$$$thereisaerrorintheexercise...$$

Answered by ajfour last updated on 21/Jun/18

$$r^2=z\overline{z}=5$$$$\mid \frac{z}{\overline{z}}\mid =\mid -1+i\frac{12}{5}\mid \ne 1?$$

Answered by tanmay.chaudhury50@gmail.com last updated on 21/Jun/18

$$z=x+iy$$$$\stackrel{-}{z}=x-iy$$$$z\stackrel{-}{z}=(x+iy)(x-iy=x^2+y^2=5$$$$\frac{x+iy}{x-iy}=-1+\frac{12}{5}i$$$$\frac{{(x+iy)}^2}{x^2+y^2}=-1+\frac{12}{5}i$$$$\frac{x^2-y^2+i2xy}{5}=\frac{-5+12i}{5}$$$$x^2-y^2=-5$$$$2xy=12$$$$x^2+y^2=5$$$$x^2-y^2=-5$$$$2x^2=0x=0$$$$y^2=5y=\pm \sqrt{5}$$$$$$$$sox=0y=\pm \sqrt{5}$$$$but2\left(o\right)\left(\sqrt{5}\right)=0but2xynotequalto12$$$$slplsplscheckquestion...$$$$plscheckthe$$

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