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[All Steps] Evaluate the integral ∫_C^f(z)dz where the path C is described by the trajectory Z(t)=e^it, for t ∈ [0,2pi ] for the functions f(z)=z^2

Question: Evaluate the integral

\[\int\limits_{C}^{{}}{f(z)dz}\]

where the path \(C\) is described by the trajectory \(Z(t)={{e}^{it}}\), for \(t\in [0,2\pi ]\) for the functions

  1. \(f(z)={{z}^{2}}\) .
  2. \(f(z)={{\left( {\bar{z}} \right)}^{2}}\)
  3. \(f(z)=\frac{z+1}{{{z}^{2}}}\)

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