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Complex Numbers and Complex Plane

In: Complex Analysis

Author

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  • Taras Mel’nyk

    (Taras Shevchenko National University of Kyiv, Faculty of Mathematics and Mechanics)

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.

Suggested Citation

  • Taras Mel’nyk, 2023. "Complex Numbers and Complex Plane," Springer Books, in: Complex Analysis, chapter 1, pages 1-19, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-39615-1_1
    DOI: 10.1007/978-3-031-39615-1_1
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