Complex Analysis/Exercises/Sheet 4

Exercise on Complex Analysis

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Problem (Integrals, 5 points)

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Let  ,   denote the standard parametrization of the unit circle. Determine the integral

 

Hint: Use the geometric series to express   in the form  . Then integrate term by term, using the first problem from the previous exercise sheet.

Problem (Antiderivatives, 5 points)

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Prove that there is no function   such that  .

Problem (More Integrals, 5 points)

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Let  , and let   denote the semicircle consisting of  , followed by  . Determine

 

Problem (Length, 5 points)

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Determine the length of the unit circle,  ,  .

Translation and Version Control

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This page was translated based on the following Wikiversity source page and uses the concept of Translation and Version Control for a transparent language fork in a Wikiversity:

https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Übungen/4._Zettel

  • Date: 01/14/2024