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Question Number 185371 by Mastermind last updated on 20/Jan/23

$$(1-\mathrm{z})(1-\stackrel{-}{\mathrm{z}})=?$$$$\mathrm{Where}\mathrm{z}\mathrm{is}\mathrm{the}\mathrm{complex}\mathrm{number}$$$$$$$$.$$

Answered by Frix last updated on 20/Jan/23

$$z=a+b\mathrm{i}\wedge \overline{z}=a-b\mathrm{i}$$$$\Rightarrow$$$$(1-z)(1-\overline{z})=a^2-2a+b^2+1={(a-1)}^2+b^2=$$$$={(\mathrm{real}\left(z\right)-1)}^2+{\left(\mathrm{imag}\left(z\right)\right)}^2$$

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