[JEE Main 2011] Let $\omega=e^{i\pi/3}$ and $a,b,c,x,y,z$ non-zero complex with $a+b+c=x$, $a+b\omega+c\omega^2=y$, $a+b\omega^2+c\omega=z$. Then $\dfrac{|x|^2+|y|^2+|z|^2}{|a|^2+|b|^2+|c|^2}$ equals ____
Let $\omega=e^{i\pi/3}$ and $a,b,c,x,y,z$ non-zero complex with $a+b+c=x$, $a+b\omega+c\omega^2=y$, $a+b\omega^2+c\omega=z$. Then $\dfrac{|x|^2+|y|^2+|z|^2}{|a|^2+|b|^2+|c|^2}$ equals ____
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
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Answer: $3$.
The transform is (up to scaling) a unitary DFT-type matrix, so $|x|^2+|y|^2+|z|^2=3(|a|^2+|b|^2+|c|^2)$, giving the ratio $3$.
JEE Main 2011 · Complex Numbers — verified solution by the Vidaara Team.
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