Complex Numbers from A to ...Z* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory |
Contents
Complex Numbers in Trigonometric Form | 29 |
Complex Numbers and Geometry | 53 |
More on Complex Numbers and Geometry | 89 |
OlympiadCaliber Problems | 161 |
Answers Hints and Solutions to Proposed Problems | 253 |
Glossary 307 | 306 |
| 313 | |
| 319 | |
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Common terms and phrases
algebraic angle area[ABC barycentric coordinates centroid circle circumcenter circumcircle of triangle circumradius coefficients collinear complex coordinate complex numbers complex numbers Z1 complex plane conclusion follows Consider the complex coordinates of points Corollary cyc cyc cyclic quadrilateral defined definition desired equal equation equilateral triangle Figure find first formula geometric image hence ifand integer isometry last relation Let Z1 letter the coordinate lines BC lowercase letter midpoint modulus nine-point circle nth roots obtain oriented orthocenter pedal triangle percase letter plane with origin point denoted points M1 polar representation polynomial positive integer Problem 13 Proof Proposition quadrilateral radius real numbers real product reflection relation is equivalent respectively Romanian Mathematical Olympiad roots of unity rotation rotation formula satisfies segment sin2 Theorem triangle A1A2A3 triangle ABC vectors vertices