Kortemeyer J. Complex Numbers. An Introduction for First Year Students 2022

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Kortemeyer J. Complex Numbers. An Introduction for First Year Students 2022

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Textbook in PDF format 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