[JEE Advanced 1999] For complex $z,w$, prove that $|z|^2w-|w|^2z=z-w$ if and only if $z=w$ or $z\bar w=1$.
For complex $z,w$, prove that $|z|^2w-|w|^2z=z-w$ if and only if $z=w$ or $z\bar w=1$.
1 Answer
VAVidaara Admin
✓ Vidaara Team
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· 1mo ago
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Answer: Proved.
Grouping $|z|^2w-|w|^2z-(z-w)=0$ factors as $(z-w)(z\bar w-1)=0$, so $z=w$ or $z\bar w=1$.
JEE Advanced 1999 · Complex Numbers — verified solution by the Vidaara Team.
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