1. ## Complex contour integration

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.

2. 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.

3. Originally Posted by Opalg
Why wouldn't the answer be zero under Cauchy's theorem?

4. 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.

5. because |z|^2 = zz* is not analytic
Originally Posted by davismj
Why wouldn't the answer be zero under Cauchy's theorem?

6. Originally Posted by xxp9
because |z|^2 = zz* is not analytic
duh