In this video, I discuss the rotational and scaling aspects of complex number multiplication and how both miraculously follow from the simple assumption that some object, called "i", squares to -1. I also present some animations showing the effect of complex number multiplication on a collection of random points on a two-dimensional grid.
This video was inspired by a Numberphile video made on Moire patterns, in which dots on a page are slightly rotated to reveal circular trajectories. In this video, I instead adopt the view of complex numbers to show how such patterns can be generated.
