Complex Numbers : An Introduction for First Year Students

• Autore: Kortemeyer Jörg
• Pubblicazione: Wiesbaden : , : Springer Fachmedien Wiesbaden GmbH, , 2022; ©2021
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (49 pages)
• Disciplina: 512.7/88
• Soggetto topico: Nombres complexos
• Soggetto genere / forma: Llibres electrònics
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- What You Can Find in This essential -- Preface -- Acknowledgements -- Contents -- 1 Why Complex Numbers? -- 2 Cartesian Representation-Algebra and Geometry of Complex Numbers -- 2.1 Introduction of the Representation Form -- 2.2 Calculations with Complex Numbers -- 2.2.1 Basic Arithmetic Operations -- 2.2.2 Solutions of Polynomial Equations of Higher Degree -- 2.2.3 Exponentiation of Complex Numbers in Cartesian Representation -- 2.3 Geometric Representations of Complex Numbers in the Gaussian Number Plane -- 3 Two Further Representations: From the Polar Form to the Euler Form -- 3.1 Refresher Course on Trigonometry -- 3.2 The Polar Form -- 3.2.1 Multiplication and Division in Polar Form -- 3.2.2 Exponentiation of Complex Numbers in Polar Form -- 3.3 Relationship Between Exponential Functions and Trigonometric Functions -- 3.4 The Euler Form -- 4 Complex Root Extraction-Moivre's Theorem -- 4.1 Preliminary Considerations -- 4.2 The Moivre Theorem -- What You Learned From This essential -- References.
• Sommario/riassunto: 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.
• Titolo autorizzato: Complex Numbers
• ISBN: 9783658349295
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910520088203321
• Lo trovi qui: Univ. Federico II
• Serie: Essentials