It is impossible to imagine modern mathematics without complex numbers. "Complex Numbers from A to ...Z" introduces the reader to this fascinating subject which, from the time of L. Euler, has become one of the most utilized ideas in mathematics.
The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them.
The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. A special feature of the book is the last chapter, a selection of real outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented.
The book reflects the unique experience of the authors. It distills a vast mathematical literature, most of which is unknown to the western public, and captures the essence of an abundant problem culture.
Author(s): Titu Andreescu, Dorin Andrica
Edition: 1
Publisher: Birkhäuser Boston
Year: 2005
Language: English
Pages: 336
cover......Page 1
About the Authors......Page 7
Complex Numbers from A to. . . Z......Page 8
Contents......Page 10
Preface......Page 14
Notation......Page 17
1 Complex Numbers in Algebraic Form......Page 18
2 Complex Numbersin Trigonometric Form......Page 45
3 Complex Numbers and Geometry......Page 69
4 More on Complex Numbers and Geometry......Page 105
5 Olympiad-Caliber Problems......Page 177
6 Answers, Hints and Solutions to Proposed Problems......Page 269
Glossary......Page 322
References......Page 328
Index of Authors......Page 332
Subject Index......Page 334
