(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If w is a complex cube root of 1, prove that x + wy + w^2z is a factor of x^3+ y^3 + z^3 - 3xyz, and hence factorise the equation completely.

2. Relevant equations

Complex cube root of 1 = -1/2 +/- 3^1/2/2 i

3. The attempt at a solution

Erm, I feel way over my head. I have tried plugging in the equation to the first one but this doesn't seem to generate anything intelligible for me.

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# Complex cube root of 1

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