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Let $z=x+iy$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE?

  1. The residue of $\frac{z}{z^2-1}$ at $z=1$ is $1/2$
  2. $\oint_C z^2 dz=0$
  3. $\frac{1}{2 \pi i} \oint_C \frac{1}{z} dz =1$
  4. $\overline{z}$ (complex conjugate of $z$ is an analytical function
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