1. ## complex numbers

if W is a non real root of the equation z^3 =1 show that x^3 +y^3 =(x+Wy)[x+(w^2)y](x+y)

i tried multiplying it out but i got no where

2. ## Re: complex numbers

Originally Posted by edwardkiely
if W is a non real root of the equation z^3 =1 show that x^3 +y^3 =(x+Wy)[x+(w^2)y](x+y)
What are $x~\&~y~?$ Do you mean that $x=\mathcal(Re)(W)~\&~y=\mathcal(Im)(W)~?$

3. ## Re: complex numbers

If nothing else you can alway find the two complex roots of $z^3-1$ and just substitute them in for $W$ and grind through the algebra.

There is almost certainly a more clever way to go about it but that will solve the problem for you.

4. ## Re: complex numbers

Originally Posted by Plato
What are $x~\&~y~?$ Do you mean that $x=\mathcal(Re)(W)~\&~y=\mathcal(Im)(W)~?$
I think $x$ and $y$ are just arbitrary numbers.

5. ## Re: complex numbers

x and y are not complex numbers. they are just unknowns. i know w=cos[0+n(120)] + isin[0+n(120)] = cos(120)+isin(120) . i know this as n=1 as this is the first non real root. what i typed out in the OP was the exact question.

6. ## Re: complex numbers

Originally Posted by Plato
What are $x~\&~y~?$ Do you mean that $x=\mathcal(Re)(W)~\&~y=\mathcal(Im)(W)~?$
Originally Posted by romsek
I think $x$ and $y$ are just arbitrary numbers.
If $W=\frac{-1}{2}+\frac{\sqrt3}{2}i$ it is true. SEE HERE