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If 1,x(1),x(2),x(3) are the roots of x^(...

If `1,x_(1),x_(2),x_(3)` are the roots of `x^(4)-1=0andomega` is a complex cube root of unity, find the value of `((omega^(2)-x_(1))(omega^(2)-x_(2))(omega^(2)-x_(3)))/((omega-x_(1))(omega-x_(2))(omega-x_(3)))`

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Knowledge Check

  • If omega is a complex cube root of unity, then what is the value of 1-(1)/((1+omega))-(1)/((1+omega^(2))) ?

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

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    B
    6
    C
    64
    D
    128

  • If omega is complex cube root of unity, then the value of (1 + 2 omega )^(-1) + (2 + omega )^(-1) - (1 + omega ) ^(-1) =

    A
    2
    B
    1
    C
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    D
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