I also like it because I had no idea how to do calculus when I created it about a year and a half ago.
I like this one because of the simplicity. To rotate an entire curve (as opposed to a single point), I made a parametric function of $t$ and applied the transformation to each point $(t, f(t))$ in the domain $a\leq t \leq b$. In the Desmos graph I took advantage of this fact to rotate each point. Luckily, the parameterization of the complex unit circle is exactly the same as the parameterization of the unit circle in the real plane (excluding the imaginary unit of course). Unfortunately, Desmos does not support complex numbers. This means a $z$ can be rotated about the origin $a$ radians by multiplying by $i^$) and $\theta$ is the angle of the same vector with the positive x axis. Note that this means each “point” is really just a single number. The blue curve is the original function and the orange curves are the rotated versions.Ī complex number $z=x+yi$ is plotted in the complex plane by putting the real part $x$ on the horizontal axis and the imaginary part $y$ on the vertical axis. I accomplished this by first looking to rotations in the complex plane, then translating the method to the real plane. The goal of this graph is to take a function $f(x)$ and rotate it around the origin by an arbitrary radian amount in order to demonstrate the concept of rotation in the complex plane. You can click on the links after each header to edit and interact with the graphs in the browser. There are some additional interesting graphs at the bottom that are cool as well. Recently I went through my old Desmos ( ) graphs and I’d like to share 5 of my favorites here.