Let - -ei2-3- and a- b- c- x- y- z be non-zero complex numbers such that a-b-c-x a-b-c-2-y a-b-2-c-z-Then the value of -x-2-y-2-z-2-a-2-b-2-c-2 is

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Standard XII

Mathematics

Harmonic Mean

Let ω =ei...

Question

Let $ω$ $= e^{i 2 π / 3}$ , and $a, b, c, x, y, z$ be non-zero complex numbers such that
$a + b + c = x$
$a + b ω + c ω^{2} = y$
$a + b ω^{2} + c ω = z$ .
Then the value of $\frac{| x |^{2} + | y |^{2} + | z |^{2}}{| a |^{2} + | b |^{2} + | c |^{2}}$ is

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Solution

The correct option is C $3$

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Let ω =ei2π/3, and a, b, c, x, y, z be non-zero complex numbers such thata+b+c=xa+bω+cω2=ya+bω2+cω=z.Then the value of |x|2+|y|2+|z|2|a|2+|b|2+|c|2 is

The correct option is C 3

Let $ω$ $= e^{i 2 π / 3}$ , and $a, b, c, x, y, z$ be non-zero complex numbers such that
$a + b + c = x$
$a + b ω + c ω^{2} = y$
$a + b ω^{2} + c ω = z$ .
Then the value of $\frac{| x |^{2} + | y |^{2} + | z |^{2}}{| a |^{2} + | b |^{2} + | c |^{2}}$ is

The correct option is C $3$