Desheng Yang - Trigonometric Functions And Complex Numbers: In Mathematical Olympiad and Competitions: 1 (World Century Mathematical Olympiad Series)

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TRIGONOMETRIC
FUNCTIONS AND
COMPLEX NUMBERS

WORLD CENTURY MATHEMATICAL OLYMPIAD SERIESSeries Editor:Shan Zun (Nanjing Normal University, China)

Vol. 1

Trigonometric Functions and Complex Numbers by Desheng Yang (Shanghai Xiangming High School, China) translated by Chunhui Shen (Shanghai Xiangming High School, China)

World Century Mathematical Olympiad Series Vol. 1

TRIGONOMETRIC FUNCTIONS AND COMPLEX NUMBERS

Desheng Yangtranslated by Chunhui ShenShanghai Xiangming High School, ChinaPublished byWorld Century Publishing Corporation27 Warren Street, Suite 401-402, Hackensack, NJ 07601, USALibrary of Congress Cataloging-in-Publication DataNames: Yang, Desheng.Title: Trigonometric functions and complex numbers / Desheng Yang,Shanghai Xiangming High School, China.Description: New Jersey : World Century, 2016. | Series: World century mathematicalolympiad series ; vol. 1 | Includes bibliographical references and index.Identifiers: LCCN 2016026528 | ISBN 9781938134869 (alk. | Numbers, Complex. | Functions of complex variables.Classification: LCC QA531 .Y345 2016 | DDC 516.24/6--dc23LC record available at https://lccn.loc.gov/2016026528British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.Originally published in Chinese by Shanghai Scientific & Technological EducationPublishing House, 2010Published by arrangement with Shanghai Century Publishing Group.Copyright 2017 by World Century Publishing CorporationAll rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher.For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.Typeset by Stallion PressEmail:Printed in Singapore

Preface

The year 2016 is officially the 30th anniversary of China joining the IMO (International Mathematical Olympiad). Looking back on these 30 years, the Chinese team has made remarkable achievements: a total of 142 gold medals, 32 silver medals, 5 bronze medals, and 19 times to be the first in total score. These achievements could not be separated from all the participants in the field of Chinese Mathematical Olympiad.This series is a summary of their work, and the authors are the representative of all the participants in the Chinese Olympic mathematics. For example, Lu Hongwen, a tutor of postgraduate candidates, not only has made remarkable achievements in the field of algebraic number theory, but also very concerned about the mathematics contest. Chen Ji, who is recognized as one of the leading experts in the field of inequality. Other members are the leading figures in the current Chinese Mathematical Olympiad, such as Xiong Bin and Feng Zhigang who repeatedly served as the leader or deputy leader of Chinese IMO national team, and served as members of the Chinese Mathematical Olympiad committee. They have made a great contribution to the Chinese Mathematical Olympiad and trained a lot of talents.Based on the authors experience and original work, there are many new ideas, new problems, new solutions, and new methods in this series.Would these cause the series too hard for readers?Of course, this series has a little difficulty. But as the authors fully understand the background of these IMO problems, they have the ability to provide the contents with breathtaking lightness.However, reading is a hard work, in particular reading a math book. Never give up whatever difficulty you meet. It requires a lot of courage and strength. In this way, you not only read a classic book, but also enjoy the fun of reading.

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