Toronto Math Forum

MAT334-2018F => MAT334--Tests => Quiz-4 => Topic started by: Victor Ivrii on October 26, 2018, 05:48:15 PM

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