Explore relativistic dot products and complex numbers in this 38-minute mathematics lecture. Delve into the formal introduction of the relativistic (red) dot product in two-dimensional space, contrasting it with the familiar Euclidean (blue) dot product. Discover a third relativistic dot product, termed green, leading to a remarkable three-fold symmetry in planar geometry called Chromogeometry. Examine how this concept is embedded within the algebra of 2x2 matrices. Investigate unit circles and isometries in the context of all three geometries simultaneously. Cover topics including Euclidean and relativistic dot products, dot product matrices, perpendicularity, unit circles, and blue, red, and green rotations in chromogeometry.