02876nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003100118050001600149072001600165072002300181082001400204245010200218264004600320300003400366336002600400337002600426338003600452347002400488505023400512520130500746650001702051650001302068650002402081650001402105650001902119650001702138650001902155650001302174650002402187650001402211700003002225700002902255710003402284773002002318776003602338856004402374978-0-8176-4449-9DE-He21320180115171432.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97808176444997 a10.1007/0-8176-4449-02doi 4aQA241-247.5 7aPBH2bicssc 7aMAT0220002bisacsh04a512.722310aComplex Numbers from A to... Zh[electronic resource] /cedited by Titu Andreescu, Dorin Andrica. 1aBoston, MA :bBirkhàˆuser Boston,c2005. aXIV, 322 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aComplex 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. aIt 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. 0aMathematics. 0aAlgebra. 0aAlgebraic geometry. 0aGeometry. 0aNumber theory.14aMathematics.24aNumber Theory.24aAlgebra.24aAlgebraic Geometry.24aGeometry.1 aAndreescu, Titu.eeditor.1 aAndrica, Dorin.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978081764326340uhttp://dx.doi.org/10.1007/0-8176-4449-0