Let $z$ and $w$ be two distinct non-zero complex numbers if $|z|^2 w-|w|^2 z=z-w$, then

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Aicharya · Accepted Answer

$\begin{array}{ll} & \left(|z|^2+1ight) w=\left(|w|^2+1ight) z \ 	herefore & 	ext { Let } z=k w, k 
eq 1, k 
eq 0 \ 	herefore & k^2|w|^2 w-k|w|^2 w=k w-w \ 	herefore & k|w|^2 w(k-1)=(k-1) w \ \Rightarrow & k=\frac{1}{|w|^2} \ 	herefore & z=\frac{w}{|w|^2} \ & \quad z \bar{w}=\frac{w}{|w|^2} \cdot \bar{w}=\frac{|w|^2}{|w|^2}=1\end{array}$

Let $z$ and $w$ be two distinct non-zero complex numbers if $|z|^2 w-|w|^2 z=z-w$, then

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