( 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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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 $\displaystyle \displaystyle z$.
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