Find all complex z = (x,y) such that [tex]z^2 + z + 1 = 0[/tex](adsbygoogle = window.adsbygoogle || []).push({});

I conclude that there is no solution set because for the real component to be 0 one must be able to solve [tex] x^2 + x + 1 = 0 [/tex] and such a solution does not exist in the reals.

Am I correct or did I mess up in my algebra some where resulting in the quadratic above?

Thanks

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# Am I right in this conclusion

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