Complex Numbers from A to ... Z

It is impossible to imagine modern mathematics without complex numbers. The second edition of __Complex Numbers from A to ... Z__ introduces the reader to this fascinating subject that 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. Many new problems and solutions have been added in this second edition. A special feature of the book is the last chapter a selection of 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. The target audience includes undergraduate high school students and their teacher's mathematical contestants (such as those training for Olympiads or the W. L. Putnam Mathematical Competition) and their coaches as well as anyone interested in essential mathematics. It is impossible to imagine modern mathematics without complex numbers. The second edition of Complex Numbers from A to ... Z introduces the reader to this fascinating subject that, 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. Many new problems and solutions have been added in this second edition. A special feature of the book is the last chapter, a selection of 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. The target audience includes undergraduates, high school students and their teachers, mathematical contestants (such as those training for Olympiads or the W. L. Putnam Mathematical Competition) and their coaches, as well as anyone interested in essential mathematics. Preface -- Complex Numbers in Algebraic Form -- Complex Numbers in Trigonometric Form -- Complex Numbers and Geometry -- More on Complex Numbers and Geometry -- Olympiad-Caliber Problems -- Answers, Hints and Solutions to Proposed Problems -- Glossary -- References -- Index of Authors. by Titu Andreescu, Dorin Andrica. "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. The target audience includes undergraduates, high school students and their teachers, mathematical contestants (such as those training for Olympiads or the W.L. Putnam Mathematical Competition) and their coaches, as well as anyone interested in essential mathematics."--Page 4 of cover "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. The target audience includes undergraduates, high school students and their teachers, mathematical contestants (such as those training for Olympiads or the W.L. Putnam Mathematical Competition) and their coaches, as well as anyone interested in essential mathematics."--Jacket * Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory Front Matter....Pages i-xvii Complex Numbers in Algebraic Form....Pages 1-30 Complex Numbers in Trigonometric Form....Pages 31-56 Complex Numbers and Geometry....Pages 57-95 More on Complex Numbers and Geometry....Pages 97-174 Olympiad-Caliber Problems....Pages 175-275 Answers, Hints, and Solutions to Proposed Problems....Pages 277-376 Back Matter....Pages 377-391