I'm going through a complex analysis question that says : Let R be a positive real number greater than $2$, let $γ_1$ : [−R,R] → $\mathbb{C}$ be defined by $γ_1$= t, let γ$_2$ = $S$($0$, R) and let $γ$ = $γ_1$ ⊕ $γ_2$. By using Cauchy’s Residue Theorem show that $$\int_γ^\ \frac{z^2}{(z^2+1)^2} dz = \frac{\pi}2$$

After going through the problem I can see that the two poles for z are ±$i$, however in the answer it says that only $i$ is in $γ$. I was wondering what does $γ$ mean in this context, and why does it only allow $i$ to be a pole.

  • $\begingroup$ Is $S(0,R)$ the semicircle of radius $R$ in the upper half plane? $\endgroup$ – carmichael561 Apr 25 '17 at 18:11
  • 1
    $\begingroup$ I believe it does, and that's answered my question now I've thought about it. Thanks $\endgroup$ – JimmieJames Apr 25 '17 at 18:14

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