Geometry Tutorial #11 -Complex Numbers (Theory)

#IMO​ #Geometry #MathOlympiad​
In this video we discuss the sixth chapter from EGMO book “Complex Numbers”. We study this powerful bashing technique. The goal is to transform the geometry of the problem into pure algebraic relations using complex numbers.
00:00 Intro
1:53 What’s a Complex Number?
18:25 Adding and Multiplying
25:20 Rotation
31:40 Reflection
36:42 Perpendicularity
40:20 Collinearity
46:05 The Unit Circle
1:03:58 Cyclic Quads
1:06:50 Similarity
1:11:57 Intersections
1:15:00 Intersection of circles
1:17:25 Tangents
1:21:26 Deriving Simson line
1:27:22 Incenter
1:31:17 Circumcenter
01:35:01 Summary
Thanks to Arc for desigining the thumbnail.
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