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Thread: complex numbers

  1. #1
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    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
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  2. #2
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    Re: complex numbers

    Quote Originally Posted by edwardkiely View Post
    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 $x=\mathcal(Re)(W)~\&~y=\mathcal(Im)(W)~?$
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  3. #3
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    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.
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  4. #4
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    Re: complex numbers

    Quote Originally Posted by Plato View Post
    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.
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  5. #5
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    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.
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  6. #6
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    Re: complex numbers

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