Could someone please give me some help with the following question to verify Cauchy's theoreom for the following equation $f ( z ) = z ^2$ evaluated around the circular contour $ Re^{iθ}$?
How to verify Cauchy's theorem for the following equation $f ( z ) = z ^2$ evaluated around a circular contour
1
$\begingroup$
complex-analysis
cauchy-integral-formula
1 Answers
0
Hint: express the contour integral $\oint_\Gamma f(z)\; dz$ as an ordinary integral using $z = R e^{i\theta}$, $dz = iR e^{i\theta} \; d\theta$, $\theta = 0 \ldots 2\pi$.