Author Topic: Q4 TUT 0201  (Read 417 times)

Victor Ivrii

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Q4 TUT 0201
« on: October 26, 2018, 05:48:15 PM »
Evaluate the given integral using Cauchy’s Formula or Theorem. Orientation counter-clockwise:
$$
\int_{|z|=1} \frac{z\,dz} {(z-2)^2}.
$$

Jeffery Mcbride

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Re: Q4 TUT 0201
« Reply #1 on: October 26, 2018, 05:52:26 PM »
\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*}