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.

It is impossible to imagine modern mathematics without complex numbers. 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. 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.

9780817644499

10.1007/0-8176-4449-0 doi

Mathematics.

Algebra.

Algebraic geometry.

Geometry.

Number theory.

Mathematics.

Number Theory.

Algebra.

Algebraic Geometry.

Geometry.

QA241-247.5

512.7