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If 1,omega,omega^2 are the cube roots of...

If `1,omega,omega^2` are the cube roots of unity then prove the following
`i) (1-omega+omega^2) + (1+omega-omega^2)^5=32`
`ii) (x+y+z)(x+yomega+zomega^2)(x+yomega^2+zomega)=x^3+y^3+z^3-3xyz`

Text Solution

Verified by Experts

The correct Answer is:
`i) =-32(-1)=32=R.H.S.`
`ii)=x^3+y^3+z^3-3xyz=R.H.S`
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Knowledge Check

  • If 1,omega and omega^2 are the cube roots of unity , then (a+b+c) (a + b omega + comega^2) (a+ bomega^2 + comega) =

    A
    `a^3+b^3+c^3`
    B
    `a^3+b^3 + c^3-3abc`
    C
    `(a+b+c)^3 -3abc`
    D
    `a^3 +b^3 + c^3 + 3abc`

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