I have a question. Does the function $z/(z^2+1)$ have primitive function in a) $ \mathbb{C} \backslash \{-i,i\}$ b) $ \mathbb{C} \backslash [-i,i]$

I tried with Cauchy theorem but I did not do it. Thanks in advance.

  • $\begingroup$ Also an open interval is denoted with parentheses, not braces. $\endgroup$ – Ross Millikan Nov 12 '18 at 21:12
  • $\begingroup$ @RossMillikan, I think the OP means the two-point set $ \{-i,i\}$. $\endgroup$ – lhf Nov 12 '18 at 21:15
  • $\begingroup$ @lhf: probably so, thanks $\endgroup$ – Ross Millikan Nov 12 '18 at 21:17
  • $\begingroup$ It means without point $-i$ and without point $i$ in point a) $\endgroup$ – John1357 Nov 12 '18 at 21:18
  • 2
    $\begingroup$ Hint: Use residues to calculate the contour integral along a big circle that goes around both poles. $\endgroup$ – Henning Makholm Nov 12 '18 at 21:20

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