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Math Help - Complex equation: z^6 +3z^3 + 1 = 0

  1. #1
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    Complex equation: z^6 +3z^3 + 1 = 0

    ( z = x + iy) is a complex number.
    I would like to know a method to solve this type of equation:
    z^6 + 3z^3 + 1 =0
    Thank you.
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  2. #2
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    Let \displaystyle Z = z^3, then your equation becomes

    \displaystyle Z^2 + 3Z + 1 = 0.

    Solve this equation for \displaystyle Z, which you can then use to solve for \displaystyle z.
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