Complex Numbers in Geometry

✍ Scribed by Marko Radovanović

• Tongue: English
• Leaves: 53
• Series: The IMO Compendium Group Olympiad Training Materials
• Category: Library

✦ Synopsis

http://www.numberwonder.co.uk/ArnoldHagger/CNinGimo.pdf

✦ Table of Contents

Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Formulas and Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3 Complex Numbers and Vectors. Rotation . . . . . . . . . . . . . . . . . . . . . . . 3
4 The Distance. Regular Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
5 Polygons Inscribed in Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
6 Polygons Circumscribed Around Circle . . . . . . . . . . . . . . . . . . . . . . . . 6
7 The Midpoint of Arc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
8 Important Points. Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
9 Non-unique Intersections and Viete’s formulas . . . . . . . . . . . . . . . . . . . . . 8
10 Different Problems – Different Methods . . . . . . . . . . . . . . . . . . . . . . . . 8
11 Disadvantages of the Complex Number Method . . . . . . . . . . . . . . . . . . . . 10
12 Hints and Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
13 Problems for Indepent Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48