Let ω=e^iπ/3 and a,b,c,x,y,z non-zero complex with a+b+c=x, a+bω+cω²=y, a+bω²+cω=z. Then |x|²+|y|²+|z|² |a|²+|b|²+|c|² equals ____

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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[JEE Main 2011] let omega e i pi 3 and a b c x y z non

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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 ____

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VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

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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