# For which simple closed curves $\gamma$, $\int\limits_{\gamma} z^{2}+z+1\, dz=0$?

For which simple closed curves $\gamma$ is $\displaystyle\int_{\gamma} z^{2}+z+1\, dz=0$

Could someone help me through this problem?

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Do you know Cauchy's theorem? –  froggie May 10 '12 at 20:44
$z^2+z+1$ has an antiderivative in the entire complex plane.... –  N. S. May 10 '12 at 20:44
If and consider also the theorem of Jordan curve –  Daniela del Carmen May 10 '12 at 20:48
What do you mean by "If and consider"? –  GEdgar May 10 '12 at 21:05

If $f(z)$ is holomorphic, then for any closed curve $\gamma$, we have $$\int_\gamma f(z)= 0$$ As other also commented: See cauchy theorem
Also: any polynomial $f(z)$ is analytic -- or should we say holomorphic! –  bgins May 10 '12 at 21:58