Complex Analysis/Exercises/Sheet 1

Exercise in Complex Analysis

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Task (Calculations, 5 Points)

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Calculate the following complex numbers:

  1.  
  2.  
  3.  
  4.  
  5.  

Task ("Writing", 5 Points)

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In the lecture, it was discussed that   is a field. Prove the following arithmetic properties for complex numbers:

  1. Associativity of multiplication:
     
  2. Distributivity of multiplication over addition:
     

Task (Equations, 5 Points)

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Find all   that satisfy the following equations:

  1.  
  2.  
  3.  

Task (Differentiation, 5 Points)

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Check whether the following functions   are differentiable. If they are, provide their derivative.

  1.  
  2.  

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/1._Zettel

  • Date: 01/14/2024