Complex root multifunction
How it works - it easy!
You should see two planes - the left one and the right one. Grab the "A" point on the left and make a trace around the plane. A' and A'' should give a trace too. It is a visualization of complex square root. It is the inverse of , which is interesting because of the fact, that , therefore the complex square root of should be - two values! That's why you see two dots on the right. (We are simulating complex plane, numbers here are two-dimensional, so we need two planes!) The most interesting part is when you try to make a loop on the left. Try it. Explore!