By Titu Andreescu, Dorin Andrica

It's very unlikely to visualize sleek arithmetic with out complicated numbers. the second one variation of complicated Numbers from A to … Z introduces the reader to this attention-grabbing topic that, from the time of L. Euler, has turn into essentially the most applied principles in mathematics.

The exposition concentrates on key innovations after which basic effects bearing on those numbers. The reader learns how complicated numbers can be utilized to resolve algebraic equations and to appreciate the geometric interpretation of advanced numbers and the operations concerning them.

The theoretical elements of the ebook are augmented with wealthy routines and difficulties at a number of degrees of trouble. Many new difficulties and strategies were further during this moment version. a unique function of the ebook is the final bankruptcy, a range of remarkable Olympiad and different very important mathematical contest difficulties solved via making use of the equipment already presented.

The ebook displays the original event of the authors. It distills an enormous mathematical literature, such a lot of that is unknown to the western public, and captures the essence of an plentiful challenge tradition. the objective viewers contains undergraduates, highschool scholars and their lecturers, mathematical contestants (such as these education for Olympiads or the W. L. Putnam Mathematical pageant) and their coaches, in addition to a person drawn to crucial mathematics.

Review:

"The e-book is a true treasure trove of nontrivial simple key innovations and functions of complicated numbers built in a scientific demeanour with a spotlight on problem-solving concepts. a lot of the e-book is going to geometric functions, after all, yet there also are sections on polynomial equations, trigonometry, combinatorics.... difficulties represent a vital part of the e-book along theorems, lemmas and examples. the issues are embedded within the textual content through the booklet, in part as illustrations to the mentioned recommendations, partially because the checking out grounds for the recommendations simply studied, yet regularly i feel to stress the centrality of challenge fixing within the authors' global view.... The ebook is admittedly approximately fixing difficulties and constructing instruments that take advantage of houses of complicated numbers.... The reader will discover a good buy of stylish and straightforward pattern difficulties or even a better volume of technically taxing ones. The booklet offers many nice instruments to aid clear up these difficulties. because the suggestions cross, the e-book is actually From 'A to Z'." —MAA