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Let omega= e^((ipi)/3) and a, b, c, x,...

Let ` omega= e^((ipi)/3) and a, b, c, x, y, z` be non-zero complex numbers such that `a+b+c = x, a + bomega + comega^2 = y, a + bomega^2 + comega = z`.Then, the value of `(|x|^2+|y|^2|+|y|^2)/(|a|^2+|b|^2+|c|^2)`

Text Solution

Verified by Experts

The correct Answer is:
3
Priniting error `=e^i(2pi)/(3)`
Then, `(|x^2|+|y|^2+|z|^2)/(|a|^2+|b|^2+|c|^2)=3`
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Knowledge Check

  • Let omega = e ^(i pi //3) and a, b, c, x, y, z be non-zero complex numbers such that a + b + c = x , a + b omega + c omega^(2) = y , a + b omega^(2) + c omega = z Then the value of (|x|^(2)+|y|^(2)+|z|^(2))/(|a|^(2)+|b|^(2)+|c|^(2)) is

    A
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  • If x = a + b y = a omega + b omega ^(2) , z = a omega ^(2) + b omega then x^(3) + y^(3) + z^(3) =

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  • If x= b + c - 2a , y = c + a - 2 b , z = a + b -2 c then the value of x^(2) + y^(2) - z^(2) + 2xy is

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