Plane Trigonometry and Complex Numbers

The intimate relationship between trigonometry and complex numbers has been observed and used extensively for hundreds of years. This book brings trigonometry and complex numbers to students of either or both areas. The timely understanding of the subject matter within will help elevate students' chances of early contributions to the chosen field, should they elect to do so. Here the focus is on key concepts in trigonometry and complex numbers and on basic results in both areas and especially results and practices connecting them. The students learn the body of trigonometry, i.e., definitions, identities, equations, inequalities, and its use in solving various problems. They also learn what complex numbers are (e.g. the field of complex numbers), why they exist, when and how they are used, operations involving them and their geometric interpretation. In particular, the book centers on a deep relationship between complex numbers and trigonometric identities and equations via the polar form of complex numbers. Undergraduates and high school students who intend to study mathematics, physics, engineering, philosophy or psychology will find this book indispensable in the sense of insight, subject treatment, and historical perspective it offers. Teachers involved in math-clubs, preparation for mathematical contests or even everyday teaching activities will find this book useful as either text or supplementary material as it meets and exceeds the guidelines given in Mathematics Framework for California Public Schools. Over 250 solved problems span hundreds of years of written history of trigonometry and complex numbers. An equal number of carefully chosen exercises reflects the development of these areas and their connections with geometry, algebra, analysis, physics and engineering. This is especially true of chapters on solving problems in Euclidean geometry via trigonometry as well as on solving problems in trigonometry by using complex numbers. They reflect the unique perspective of the author whose teaching and research experience is in both mathematics and engineering.