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
| 2 | |
| 4 | |
Answers Hints and Solutions to Proposed Problems | 6 |
2 | 65 |
OlympiadCaliber Problems | 161 |
5 | 196 |
Glossary | 262 |
References | 313 |
| 319 | |
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Common terms and phrases
a+b+c ABCD algebraic angle area[A area[ABC argz barycentric coordinates centroid circle circumcenter circumcircle circumcircle of triangle circumradius collinear complex coordinate complex numbers complex numbers z1 complex plane Consider the complex coordinates of points Corollary desired distinct points equal equation equilateral triangle Figure formula geometric image hence Im(z integer isometry last relation Let Z1 midpoint modulus nine-point circle nth roots number z obtain oriented orthocenter pedal triangle plane with origin points M1 polar representation polygon polynomial positive integer Problem 13 Proof Proposition Prove quadrilateral Re(z real product relation is equivalent respectively Romanian Mathematical Olympiad roots of unity rotation segment sides sin2 sint Solution Theorem triangle A1 A2 triangle ABC vector vertices αβ αβγ Απ βγ γα Επ π π