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If 1, omega omega^(2) are the cube roots...

If 1, `omega omega^(2)` are the cube roots of unity then show that ` (1 + 5omega^(2) + omega^(4)) ( 1 + 5omega + omega^(2)) ( 5 + omega + omega^(5))` = 64.

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The correct Answer is:
64
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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
    `32`

  • If omega is the cube root of unity then Assertion : (1-omega+omega^(2))^(6)+(1+omega-omega^(2))^(6)=128 Reason : 1+omega+omega^(2)=0

    A
    `R` is the only clue to prove `(A)`
    B
    We can prove by expansion of each term in the LHS
    C
    `(A)` is wrong `(R )` is correct.
    D
    `omega^(3)=1` is also needed to prove `(A)`

  • If is a cubeth root of unity root of : (1-omega+omega^(2))^(4)+(1+omega-omega^(2))^(4) is :

    A
    `0`
    B
    `32`
    C
    `-16`
    D
    `-32`

    • Similar Questions

    Explore conceptually related problems

    If omega pm 1 is a cube root of unity, show that (1 - omega + omega^(2))^(6) + (1 + omega - omega^(2))^(6) = 128

    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

    If omega pm 1 is a cube root of unity, show that (1 + omega) (1 + omega^(2))(1 + omega^(4))(1 + omega^(8))…(1 + omega^(2^(11))) = 1

    If omega is a cube root of unity, then find the value of the following: (1+omega-omega^2)(1-omega+omega^2)

    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))=

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