| List of Illustrations | |
| Preface | |
| Introduction | 3 |
| Ch. 1 | The Puzzles of Imaginary Numbers | 8 |
| Ch. 2 | A First Try at Understanding the Geometry of [the square root of] -1 | 31 |
| Ch. 3 | The Puzzles Start to Clear | 48 |
| Ch. 4 | Using Complex Numbers | 84 |
| Ch. 5 | More Uses of Complex Numbers | 105 |
| Ch. 6 | Wizard Mathematics | 142 |
| Ch. 7 | The Nineteenth Century, Cauchy, and the Beginning of Complex Function Theory | 187 |
| App. A | The Fundamental Theorem of Algebra | 227 |
| App. B | The Complex Roots of a Transcendental Equation | 230 |
| App. C | ([the square root of] -1)[superscript [square root of] -1] to 135 Decimal Places, and How It Was Computed | 235 |
| Notes | 239 |
| Name Index | 251 |
| Subject Index | 255 |
| Acknowledgments | 259 |
