Let ω = e^{i\pi\/3} , and a, b, c, x, y, z be non-zero complex numbers such that a + b + c = x a + bω + c\omega^2 = y a + b\omega^2 + cω = z Then the value of \frac{|x|^2+|y|^2+|z|^2}{|a|^2+|b|^2+|c|^2} is ____. [JEE Adv 2011 P2]

Complex Numbers

Section: Mathematics

Question : 27 of 36

Marks: +1, -0

Let ω = eiπ∕3 , and a, b, c, x, y, z be non-zero complex numbers such that
a + b + c = x
a + bω + cω2 = y
a + bω2 + cω = z
Then the value of

|x|2+|y|2+|z|2

|a|2+|b|2+|c|2

is ____.

[JEE Adv 2011 P2]

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