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Chapter 18: Complex Numbers and Functions of them

Introduction

Complex numbers, their representation as points in the complex plane, and functions defined on the complex plane are of great importance in many subjects. Basic properties are reviewed.

Topics

18.1 Notations, Representation of a Complex Number by Magnitude and Angle, Real and Imaginary Parts

18.2 Functions of a Complex Variable

18.3 Functions of z, z = x + iy, have no Curl, as Vectors

18.4 De Moivre's Theorem

18.5 The Logarithm and the Problem of the Multivalued Nature of Angles