Question Number 135298 by Ahmed1hamouda last updated on 12/Mar/21
Answered by mr W last updated on 12/Mar/21
$$\mathrm{1} \\ $$$${z}={x}+{yi} \\ $$$$\frac{\mathrm{1}}{{z}}=\frac{\mathrm{1}}{{x}+{yi}}=\frac{{x}−{yi}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$$${Re}\left(\frac{\mathrm{1}}{{z}}\right)=\frac{{x}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\leqslant\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} \geqslant\mathrm{2}{x} \\ $$$$\left({x}−\mathrm{1}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} \geqslant\mathrm{1} \\ $$
Commented by mr W last updated on 12/Mar/21
Answered by mr W last updated on 12/Mar/21