Số phức từ A tới Z của Titu Andresscu (Tài liệu tiếng Anh)

About the AuthorsTitu Andreescu received his BA, MS, and PhD from the West University of Timisoara, Romania. The topic of his doctoral dissertation was “Research on Diophantine Analysis and Applications.” Professor Andreescu currently teaches at the University of Texas at Dallas. Titu is past chairman of the USA Mathematical Olympiad, served as director of the MAA American Mathematics Competitions (1998–2003), coach of the USA International Mathematical Olympiad Team (IMO) for 10 years (1993–2002), Director of the Mathematical Olympiad Summer Program (1995–2002) and leader of the USA IMO Team (1995–2002). In 2002 Titu was elected member of the IMO Advisory Board,...
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Số phức từ A tới Z của Titu Andresscu (Tài liệu tiếng Anh)About the AuthorsTitu Andreescu received his BA, MS, and PhD from the West Universityof Timisoara, Romania. The topic of his doctoral dissertation was “Researchon Diophantine Analysis and Applications.” Professor Andreescu currentlyteaches at the University of Texas at Dallas. Titu is past chairman of the USAMathematical Olympiad, served as director of the MAA American Mathemat-ics Competitions (1998–2003), coach of the USA International MathematicalOlympiad Team (IMO) for 10 years (1993–2002), Director of the Mathemat-ical Olympiad Summer Program (1995–2002) and leader of the USA IMOTeam (1995–2002). In 2002 Titu was elected member of the IMO AdvisoryBoard, the governing body of the world’s most prestigious mathematics com-petition. Titu received the Edyth May Sliffe Award for Distinguished HighSchool Mathematics Teaching from the MAA in 1994 and a “Certificate ofAppreciation” from the president of the MAA in 1995 for his outstandingservice as coach of the Mathematical Olympiad Summer Program in prepar-ing the US team for its perfect performance in Hong Kong at the 1994 IMO.Titu’s contributions to numerous textbooks and problem books are recognizedworldwide.Dorin Andrica received his PhD in 1992 from “Babes-Bolyai” University in ¸Cluj-Napoca, Romania, with a thesis on critical points and applications to thegeometry of differentiable submanifolds. Professor Andrica has been chair-man of the Department of Geometry at “Babes-Bolyai” since 1995. Dorin has ¸written and contributed to numerous mathematics textbooks, problem books,articles and scientific papers at various levels. Dorin is an invited lecturer atuniversity conferences around the world—Austria, Bulgaria, Czech Republic,Egypt, France, Germany, Greece, the Netherlands, Serbia, Turkey, and USA.He is a member of the Romanian Committee for the Mathematics Olympiadand member of editorial boards of several international journals. Dorin hasbeen a regular faculty member at the Canada–USA Mathcamps since 2001. Titu Andreescu Dorin AndricaComplex Numbers from A to. . . Z Birkh¨ user a Boston • Basel • Berlin Dorin Andrica Titu Andreescu “Babes-Bolyai” University ¸ University of Texas at Dallas Faculty of Mathematics School of Natural Sciences and Mathematics 3400 Cluj-Napoca Richardson, TX 75083 Romania U.S.A.Cover design by Mary Burgess.Mathematics Subject Classification (2000): 00A05, 00A07, 30-99, 30A99, 97U40Library of Congress Cataloging-in-Publication DataAndreescu, Titu, 1956- Complex numbers from A to–Z / Titu Andreescu, Dorin Andrica. p. cm. “Partly based on a Romanian version . . . preserving the title. . . and about 35% of the text”–Pref. Includes bibliographical references and index. ISBN 0-8176-4326-5 (acid-free paper) 1. Numbers, Complex. I. Andrica, D. (Dorin) II. Andrica, D. (Dorin) Numere complexe QA255.A558 2004 512.7’88–dc22 2004051907ISBN-10 0-8176-4326-5 eISBN 0-8176-4449-0 Printed on acid-free paper.ISBN-13 978-0-8176-4326-3 c 2006 Birkh¨ user Boston aComplex Numbers from A to. . . Z is a greatly expanded and substantially enhanced version of the Romanianedition, Numere complexe de la A la. . . Z, S.C. Editura Millenium S.R. L., Alba Iulia, Romania, 2001All rights reserved. This work may not be translated or copied in whole or in part without the writtenpermission of the publisher (Birkh¨ user Boston, c/o Springer Science+Business Media Inc., 233 Spring aStreet, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly anal-ysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computersoftware, or by similar or dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks and similar terms, even if they arenot identified as such, is not to be taken as an expression of opinion as to whether or not they are subject toproprietary rights.Printed in the United States of America. (TXQ/MP)987654321www.birkhauser.comThe shortest path between two truths in the realdomain passes through the complex domain. Jacques HadamardAbout the AuthorsTitu Andreescu received his BA, MS, and PhD from the West Universityof Timisoara, Romania. The topic of his doctoral dissertation was “Researchon Diophantine Analysis and Applications.” Professor Andreescu currentlyteaches at the University of Texas at Dallas. Titu is past chairman of the USAMathematical Olympiad, served as director of the MAA American Mathemat-ics Competitions (1998–2003), coach of the USA International MathematicalOlympiad Team (IMO) for 10 years (1993–2002), Director of the Mathemat-ical Olympiad Summer Program (1995–2002) and leader of the USA IMOTeam (1995–2002). In 2002 Titu was elected member of the IMO AdvisoryBoard, the governing body of the world’s most prestigious mathematics com-petition. Titu received the Edyth May Sliffe Award for Distinguished HighSchool Mathematics Teaching from the MAA in 1994 and a “Certificate ofAppreciation” from the president of the MAA in 1995 for his outstandingservice as coach of th ...