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If omega pm 1 is a cube root of unity, s...

If `omega pm` 1 is a cube root of unity, show that `(a + b omega + c omega^(2))/(b + c omega + a omega^(2))+ (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) = -1`

Text Solution

Verified by Experts

The correct Answer is:
` = omega + omega^(2) = -1 [ because 1 + omega omega^(2) = 0]`
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Knowledge Check

  • If omega is a cube root of unity, then the value of (1 - omega + omega^2)^4 + (1 + omega - omega^2)^(4) is ……….

    A
    `-16`
    B
    `0`
    C
    `-32`
    D
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  • If omega is a complex cube root of unity, then (a+b omega+c omega^(2))/(c+a omega+b omega^(2))+(c+a omega+b omega^(2))/(a +b omega+c omega^(2))+(b+c omega+a omega^(2))/(b+c omega+a omega^(5))=

    A
    `1`
    B
    `omega`
    C
    `omega^(2)`
    D
    `0`

  • If omega is a non real cube root of unity, then (a+b)(a+b omega)(a+b omega^2)=

    A
    `a^(3)+b^(3)`
    B
    `a^(3)-b^(3)`
    C
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    D
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    If omega is a cube root of unity, then find the value of the following: (1+omega-omega^2)(1-omega+omega^2)

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