The beauty of complex functions

A compilation of plots of different complex functions, like adding and multiplying complex constants, exponentiation, the power function (including nth roots), and logarithm. Issues like branch cuts, branch points, and branches in general will also be discussed as the result of inability to construct the plots. Finally, we will do a 4D rotation (composed of two 4D reflections) to the typical Riemann surfaces pictures, and see that it should be the same as its inverse functions. The video is going to be jam-packed with visuals and animations, so while it may sometimes be too quick, you can pause the video; or you can just simply appreciate the visuals, the plots, and the animations. Some interesting plots are usually the vector plots, like for the power functions, we have different regions of flow. The formula of 2(n 1) when n is positive can be left as an exercise - it is not TOO difficult to see why, but it is not the focus of the video, or not the primary feature that I want to discuss; or for negative po