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Question Number 135298 by Ahmed1hamouda last updated on 12/Mar/21

Answered by mr W last updated on 12/Mar/21

$$1$$$$z=x+yi$$$$\frac{1}{z}=\frac{1}{x+yi}=\frac{x-yi}{x^2+y^2}$$$$Re\left(\frac{1}{z}\right)=\frac{x}{x^2+y^2}⩽\frac{1}{2}$$$$x^2+y^2⩾2x$$$${(x-1)}^2+y^2⩾1$$

Commented by mr W last updated on 12/Mar/21

Answered by mr W last updated on 12/Mar/21

$$2$$$$z=x+yi$$$$\stackrel{-}{z}=x-yi$$$$z-\stackrel{-}{z}=2yi$$$$\frac{z-\overline{z}}{2i}=y=Im\left(z\right)$$

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