Complex contour integration

**Eudaimonia** · April 2nd 2010, 04:56 PM

Let $\gamma$ be the square with vertices 0, 1, $\imath+1$ , $\imath$ traversed counterclockwise. Evaluate
$\int_{\gamma}{|z|^2dz}$ .

I parametrized and then deduced the formula:
$\int _{\gamma }\left|z|^2dz\right.=\sum _{i=1}^4 \int _{\gamma _i}|\gamma _i(t)|^2\gamma _i'(t)dt$ . I come up with -1+ $\imath$ as the answer. Please verify, thank you.

**Opalg** · April 3rd 2010, 11:14 AM

Originally Posted by Eudaimonia

Let $\gamma$ be the square with vertices 0, 1, $i+1$ , $i$ traversed counterclockwise. Evaluate
$\int_{\gamma}{|z|^2dz}$ .

I parametrized and then deduced the formula:
$\int _{\gamma }\left|z|^2dz\right.=\sum _{i=1}^4 \int _{\gamma _i}|\gamma _i(t)|^2\gamma _i'(t)dt$ . I come up with $-1+i$ as the answer. Please verify, thank you.

I agree with your answer.

**davismj** · April 3rd 2010, 03:49 PM

Originally Posted by Opalg

I agree with your answer.

Why wouldn't the answer be zero under Cauchy's theorem?

**Eudaimonia** · April 3rd 2010, 04:36 PM

Please correct me if I'm wrong, but I don't think f(z)=|z|^2 is holomorphic at 0, and thus it does not meet that requirement of Cauchy's integral theorem.

**xxp9** · April 3rd 2010, 04:43 PM

because |z|^2 = zz* is not analytic

Originally Posted by davismj

Why wouldn't the answer be zero under Cauchy's theorem?

**davismj** · April 3rd 2010, 05:21 PM

Originally Posted by xxp9

because |z|^2 = zz* is not analytic

duh

Thread: Complex contour integration

LinkBack

Thread Tools

Display

Complex contour integration

Similar Math Help Forum Discussions

Complex Contour Integration With Branch Cut

Complex Contour Integrals

Complex Contour Integral

Complex Contour Integral

Complex Contour Question

Search Tags