Complex Numbers and Complex Plane

Taras Mel’nyk
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Taras Mel’nyk: Taras Shevchenko National University of Kyiv, Faculty of Mathematics and Mechanics

Chapter 1 in Complex Analysis, 2023, pp 1-19 from Springer

Abstract: Abstract In this chapter we recall some concepts from basic courses in mathematical analysis of real-valued functions of one and several variables as well as from a course in linear algebra, namely complex numbers and their various forms, arithmetic operations on them (Sect. 1.1), and basic topological notions in the vector space ℝ 2 $$\mathbb R^2$$ (Sect. 1.5). The novel notion of the stereographic projection in Sect. 1.2 provides a geometric interpretation of the extended complex plane. Complex-valued functions of a real variable and various curves in the complex plane are considered in more detail in Sects. 1.3 and 1.4, respectively.

Date: 2023
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DOI: 10.1007/978-3-031-39615-1_1

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