Title Details: | |
The Real and the Complex numbers |
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Authors: |
Varsos, Dimitrios |
Description: | |
Abstract: |
In the seventh chapter, the real numbers are introduced. There are many ways to define real numbers. Here we prefer a way that "flows more naturally". Specifically, the rational numbers are extended to the real numbers. This is achieved using the Dedekind cuts. We point out the fundamental difference between rational and real numbers (the completeness principle). In the second part of the chapter, the field of complex numbers is defined. The geometric representation of the complex numbers with Cartesian and polar coordinates is presented and the roots of the unity are studied. Finally, the expression of complex numbers in exponential form is presented.
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Linguistic Editors: |
Kalliaras, Dimitrios |
Technical Editors: |
Paschalis, Vasilis |
Graphic Editors: |
Paschalis, Vasilis |
Type: |
Chapter |
Creation Date: | 20-09-2023 |
Item Details: | |
License: |
Attribution - NonCommercial - ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
Handle | http://hdl.handle.net/11419/10618 |
Bibliographic Reference: | Varsos, D. (2023). The Real and the Complex numbers [Chapter]. In Varsos, D. 2023. Elements of Advanced Mathematics [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/10618 |
Language: |
Greek |
Is Part of: |
Elements of Advanced Mathematics |
Publication Origin: |
Kallipos, Open Academic Editions |