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Complex numbers are a typical topic of basic mathematics courses. This essential provides a detailed introduction and presentation of essential aspects of dealing with complex numbers, on the one hand related to commonly occurring tasks and on the other hand embedded in basic mathematical content. This Springer essential is a translation of the original German 1st edition essentials Komplexe Zahlen by Jörg Kortemeyer, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
What You Can Find in This essential
Preface
Acknowledgements
Why Complex Numbers?
Cartesian Representation—Algebra and Geometry of Complex Numbers
Introduction of the Representation Form
Calculations with Complex Numbers
Basic Arithmetic Operations
Solutions of Polynomial Equations of Higher Degree
Exponentiation of Complex Numbers in Cartesian Representation
Geometric Representations of Complex Numbers in the Gaussian Number Plane
Two Further Representations: From the Polar Form to the Euler Form
Refresher Course on Trigonometry
The Polar Form
Multiplication and Division in Polar Form
Exponentiation of Complex Numbers in Polar Form
Relationship Between Exponential Functions and Trigonometric Functions
The Euler Form
Complex Root Extraction—Moivre’s Theorem
Preliminary Considerations
The Moivre Theorem
What You Learned From This essential
References