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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 in 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. The Content Introduction and discussion of the three representations of complex numbers: Cartesian representation, polar representation, Euler representation Elaboration of essential basics and extension of these for dealing with complex numbers Supporting thematization of the view as well as the potentials of representation changes Pointing out of deepenings as connection points to the further topics from basic lectures on mathematics The Target Groups Students of engineering and natural sciences for a closer examination of the topic; STEM freshmen before entering university for the development of their school knowledge with regard to a successful entry into university. Students who want to independently explore a topic outside the school curriculum that has many connections to familiar school content. The Author Jörg Kortemeyer holds a PhD from the Centre for Higher Mathematics Education (khdm: Kompetenzzentrum Hochschuldidaktik Mathematik) and has been active for more than ten years in teaching mathematics to engineering students as well as other study programs including mathematical pre-courses. Since 2018, he has been working at Clausthal University of Technology on improving the entry into STEM subjects and economics.

Mathematics --- wiskunde --- Nombres complexos

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Quaternions --- Àlgebra universal --- Cinemàtica --- Corbes --- Superfícies (Matemàtica) --- Anàlisi vectorial --- Nombres complexos --- Functions, Quaternion. --- Quaternion functions --- Functions of complex variables

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Varietats algebraiques --- Àlgebra universal --- Àlgebra --- Àlgebra lineal --- Anàlisi vectorial --- Categories (Matemàtica) --- Matrius (Matemàtica) --- Quaternions --- Nombres complexos --- Varietats algèbriques --- Geometria algebraica --- Varietats tòriques --- Grups algebraics lineals --- Quasivarieties (Universal algebra) --- Algebraic systems, Quasi-varieties of --- Classes, Implicationally defined --- Classes, Quasi-primitive --- Classes, Universal Horn --- Horn classes, Universal --- Implicationally defined classes --- Quasi-primitive classes --- Quasi-varieties of algebraic systems --- Quasiprimitive classes --- Universal Horn classes --- Varieties (Universal algebra) --- Logic, Symbolic and mathematical