[tex]z^2+z+1=0[/tex]
z(z+1) = -1
[tex]z+1 = \frac{-1}{z} [/tex]
[tex]z+1+ \frac{1}{z} = 0 =\ \textgreater \ z + \frac{1}{z} = -1[/tex]
[tex]z+ \frac{1}{z} = -1 | ^2[/tex]
[tex]z^2 + \frac{1}{z^2} + 2 = 1[/tex]
[tex]z^2 + \frac{1}{z^2} = -1[/tex]
[tex]z^2 + \frac{1}{z^2} = -1 |^2 [/tex]
[tex]z^4 + \frac{1}{z^4} +2 = 1 [/tex]
[tex]z^4 + \frac{1}{z^4} = -1[/tex]
