Contents
Preface to the Second Edition ix
Preface to the First Edition xi
Chapter I. Complex Numbers 1
§I.1. Definition of C 2
§I.2. Field Axioms 2
§I.3. Embedding of R in C. The Imaginary Unit 3
§I.4. Geometric Representation 3
§I.5. Triangle Inequality 4
§I.6. Parallelogram Equality 5
§I.7. Plane Geometry via Complex Numbers 5
§I.8. C as a Metric Space 6
§I.9. Polar Form 6
§I.10. De Moivre’s Formula 7
§I.11. Roots 8
§I.12. Stereographic Projection 9
§I.13. Spherical Metric 10
§I.14. Extended Complex Plane 11
Chapter II. Complex Differentiation 13
§II.1. Definition of the Derivative 13
§II.2. Restatement in Terms of Linear Approximation 14
§II.3. Immediate Consequences 14
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