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

• March 29th 2011, 07:49 PM
hurz
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.
• March 29th 2011, 07:52 PM
Prove It
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 $\displaystyle z$.