Q4 TUT 0201

[Victor Ivrii]

Evaluate the given integral using Cauchy’s Formula or Theorem. Orientation counter-clockwise:
$$
\int_{|z|=1} \frac{z\,dz} {(z-2)^2}.
$$

[Jeffery Mcbride]

\begin{equation*}
This\ formula\ cannot\ be\ re-written\ with\ Cauchy's\ formula,\ so\ we\ use\ Cauchy's\ theorem.\\
\\
\int _{|z|\ =\ 1} f( z) dz\ =\ 0\\
\\
\int _{|z|\ =\ 1} \ \frac{z}{( z-2)^{2}} \ dz\ =\ 0\\
\end{equation*}