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The value of the following complex integral, with $\text{C}$ representing the unit circle

centered at origin in the counterclockwise sense, is:

$$\int _{C}\frac{z^{2}+1}{z^{2}-2z}\:dz$$

  1. $8\pi i$
  2. $-8\pi i$
  3. $-\pi i$
  4. $\pi i$
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