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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.
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