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Math Help - Complex number problem

  1. #1
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    Complex number problem

    Just wondering how i would solve (z^6) -2(z^3) +4 = 0 (where z is a complex number)

    any help would be greatly appreciated.

    Shaun
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Shaun Gill
    Just wondering how i would solve (z^6) -2(z^3) +4 = 0 (where z is a complex number)

    any help would be greatly appreciated.

    Shaun
    Stage 1: Treat it as a quadratic in z^3 and use the quadratic
    formula.

    This will give you two complex roots.

    Stage 2:Convert each of the roots into polar form (that is write w
    as: w=|w|\ e^{\bold{i}\theta}, then:

    <br />
w^{\frac{1}{3}}=|w|^{\frac{1}{3}}\ e^{\bold{i}\theta/3}\ \wedge\  |w|^{\frac{1}{3}}\ e^{\bold{i}(\theta/3+2\pi/3)}\ \wedge\  |w|^{\frac{1}{3}}\ e^{\bold{i}(\theta/3+4\pi/3)}<br />

    RonL
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  3. #3
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    thanx a lot. genius.
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