Chapters in this book

1. Frontmatter i
2. A Note to the Reader vii
3. Contents ix
4. List of Illustrations xi
5. Preface to the Paperback Edition xiii
6. Preface xxi
7. An Imaginary Tale
8. Introduction 3
9. CHAPTER ONE The Puzzles of Imaginary Numbers 8
10. CHAPTER TWO. A First Try at Understanding the Geometry of √-1 31
11. CHAPTER THREE The Puzzles Start to Clear 48
12. CHAPTER FOUR Using Complex Numbers 84
13. CHAPTER FIVE More Uses of Complex Numbers 105
14. CHAPTER SIX Wizard Mathematics 142
15. CHAPTER SEVEN The Nineteenth Century, Cauchy, and the Beginning of Complex Function Theory 187
16. APPENDIX A. The Fundamental Theorem of Algebra 227
17. APPENDIX B. The Complex Roots of a Transcendental Equation 230
18. APPENDIX C. (√-1)(√-1) to 135 Decimal Places, and How It Was Computed 235
19. APPENDIX D. Solving Clausen’s Puzzle 238
20. APPENDIX E. Deriving the Differential Equation for the Phase-Shift Oscillator 240
21. APPENDIX F. The Value of the Gamma Function on the Critical Line 244
22. Notes 247
23. Name Index 261
24. Subject Index 265
25. Acknowledgments 269