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A Guide to Complex Variables
Steven G. Krantz October 14, 2007

iii

To Paul Painlev´ (18631933). e

Table of Contents

Preface 1 The Complex Plane 1.1 Complex Arithmetic . . . . . . . . . . . . . . . . . . . . . 1.1.1 The Real Numbers . . . . . . . . . . . . . . . . . . 1.1.2 The Complex Numbers . . . . . . . . . . . . . . . . 1.1.3 Complex Conjugate . . . . . . . . . . . . . . . . . . 1.1.4 Modulus of a Complex Number . . . . . . . . . . . 1.1.5 The Topology of the Complex Plane . . .

A Guide to Complex Variables
Steven G. Krantz October 14, 2007

iii

To Paul Painlev´ (18631933). e

Table of Contents

Preface 1 The Complex Plane 1.1 Complex Arithmetic . . . . . . . . . . . . . . . . . . . . . 1.1.1 The Real Numbers . . . . . . . . . . . . . . . . . . 1.1.2 The Complex Numbers . . . . . . . . . . . . . . . . 1.1.3 Compl…(skip)

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