Complex Analysis/Exercises/Sheet 5: Revision history

14 January 2025

• curprev 13:4213:42, 14 January 2025 imported>Eshaa2024 1,658 bytes +1,658 New resource with "== Exercise on Complex Analysis == ==== Problem (Integrals, 5 points) ==== Calculate the following integrals using the Cauchy integral formula: # <math>\int_{|z+1| = 1} \frac{dz}{(z+1)(z-1)^3}</math> # <math>\int_{|z|=2} \frac{\sin z}{z+i}\, dz</math> # <math>\int_{|z|=r} \frac{dz}{(z-a)^n(z-b)^m}</math> mit <math>|a| < r < |b|</math>, <math>n,m \ge 1</math>. ==== Problem (Cauchy, 10 points) ==== Let <math>S^1 := \{z \in \mathbf C: |z| = 1\}</math>. On <math>\mathbf C \s..."