03439nam 22004933 450 991052008820332120260605205230.09783658349295(electronic bk.)(MiAaPQ)EBC6838855(Au-PeEL)EBL6838855(CKB)20275199600041(PPN)259387347(BIP)82727962(iGPub)SPNA0085375(OCoLC)1333082672(EXLCZ)992027519960004120220104d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierComplex Numbers An Introduction for First Year Students1st ed.Wiesbaden :Springer Fachmedien Wiesbaden GmbH,2022.©2021.1 online resource (49 pages)Essentials Print version: Kortemeyer, Jörg Complex Numbers Wiesbaden : Springer Fachmedien Wiesbaden GmbH,c2022 9783658349288 Includes bibliographical references and index.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.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.Essentials Nombres complexosthubLlibres electrònicsthubNombres complexos512.7/88Kortemeyer Jörg1074745MiAaPQMiAaPQMiAaPQ9910520088203321Complex Numbers2581439UNINA