query: how to deal with $| dz |$ in complex integral, with two examples
positive_passages.docid: 16820
positive_passages.text: Evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle
negative_passages.docid: 80650
negative_passages.text: Complex differentiability of $f(z)=|z|$
negative_passages.docid: 39380
negative_passages.text: How do I visualize $\exp(z)$ as a complex mapping?
negative_passages.docid: 27347
negative_passages.text: Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
negative_passages.docid: 31777
negative_passages.text: Complex line integral
negative_passages.docid: 138329
negative_passages.text: Complex Analysis analytic function problem
negative_passages.docid: 61466
negative_passages.text: what is $\int_{|z|=3}\frac{1}{(z-2)^n(z-4)^m}dz$ for $m,n\in\mathbb{N}$?
negative_passages.docid: 15482
negative_passages.text: Paths integrals in the complex plane
negative_passages.docid: 89601
negative_passages.text: Rusty at complex integrals, finding error in steps
negative_passages.docid: 136359
negative_passages.text: How to define a complex function with assumptions?
negative_passages.docid: 137045
negative_passages.text: The estimate of real and imaginary part of a holomorphic function
negative_passages.docid: 51216
negative_passages.text: Different ways to tackle the integral $\int_0^1\sqrt\frac x{1-x}\,dx$
negative_passages.docid: 109857
negative_passages.text: Contour integral of analytic function with singularity
negative_passages.docid: 96023
negative_passages.text: Prove: $\int_\gamma \bar z \, dz=2i\operatorname{Area}(G)$
negative_passages.docid: 43506
negative_passages.text: Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$
negative_passages.docid: 107146
negative_passages.text: How can i prove this problem about Cauchy integral?
negative_passages.docid: 100559
negative_passages.text: Gaussian integral with a shift in the complex plane