( z = x + iy) is a complex number.

I would like to know a method to solve this type of equation:

$\displaystyle z^6 + 3z^3 + 1 =0$

Thank you.

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- Mar 29th 2011, 06:49 PMhurzComplex 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:

$\displaystyle z^6 + 3z^3 + 1 =0$

Thank you. - Mar 29th 2011, 06:52 PMProve It
Let $\displaystyle \displaystyle Z = z^3$, then your equation becomes

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

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