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omega is an imaginary root of unity. ...

`omega` is an imaginary root of unity.
Prove that
If `a+b+c = 0` then prove that `(a + bomega + comega^(2))^(3)+(a+bomega^(2) + comega)^(3) = 27abc`.

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`a+ b+c=0`
. `rArr b+c = -a,c+a= -b` and `a+ b= -c`
Putting these values of the R.H.S of result (i), we get
`(a+ bomega + comega^(2))^(3) + (a+bomega^(2)+ comega)^(3) = 27abc`
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