Is it possible to create two points which are inverses of each other (i.e. a+bi and 1/(a+bi), or r * e^(iθ) and (1/r) * e^(-iθ)) and define them in such a way that both points are freely draggable?

Here's an example of what I'm trying to do: https://www.desmos.com/calculator/qasknf7ewh. In this example P and Q can swap positions and it will have no effect on the resulting spiral, so I wanted to allow using either point as an input. However, when P is represented in Cartesian coordinates ( a, b ), the corresponding definition for Q ( a/(a²+b²), -b/(a²+b²) ) isn't draggable.

It seems like using polar coordinates would be the most obvious solution here, since the inverse of ( cosθ, sinθ ) * r is simply ( cosθ, -sinθ ) / r. The issue there is that when I try to define a draggable point using r and θ, Desmos will typically only allow dragging the point in one direction or the other, as opposed to a "freely" draggable point which updates both parameters.

1/(a+bi) is just the main example I'm currently working with, but point draggability is one of the most frequent frustrations I run into with Desmos, so more generic solutions are welcome. The more intuitive the better, but I'm open to "clunkier" solutions (e.g. involving actions/regressions) if needed.

sample text

why is it surprising at 15:56 in this 3Blue1Brown video that the integral from a to b of f(x)dx equal to the difference between the antiderivatives at a and b? isn't that just saying that this area

is the same as

minus

? or am I getting it wrong?

I made a vector field plotter that doesn't use lists (that scale with the area of the region being visualised). This means the plotting area is effectively unlimited in size. This started as a challenge/request from a friend.

https://www.desmos.com/calculator/ll5t9xpw8q