Riemann • Complex Functions

This page is set up to accompany a video that covered the basics of the complex number plane, made by considering magnitude not just as length, but also including direction. With an idea of the complex number plane, we looked at squaring, and found that the inverse, taking a square root, is a question that has two answers everywhere but zero.

Interactive Animation

This animation requires the Wolfram CDF player:

  • Movable Squaring Path — When the path does not include the center point (the origin), the double-sheeted nature of square roots doesn't come up.


A short additional video of some Q&A on how complex (vector) multiplication works: (download)