As far as I know, Desmos doesn’t show complex graphs (i.e. graphs in the complex plane), so in that sense the answer would be no.
@Max_S’s link in Post 15 shows the 6 solutions in Desmos, but he had to translate them into points on a circle in the real plane.
@Zoobi’s plot is part of what Wolfram Alpha gives you if you enter the equation (x-2)^6 = 729.
Desmos has started implementing complex features, within the past year or so. It wouldn’t surprise me if they implement a complex graphing mode soon. But so far as I know, they haven’t yet. Though I have seen some user-made scripts that approximate it.
If it is understood that you are working in the real plane (it could have been three dimensions, for instance; is there a menu option?) and you type in an equation f(x,y)=0, then it should plot the set of points satisfying f(x,y)=0. What else would you expect?
It’s fine.
One way is to map magnitude to brightness and argument to hue:
https://doc.sagemath.org/html/en/reference/plotting/_images/complex_plot-6.svg
Well, that’s certainly the best response of a graphing program to typing in an equation like that. It’s not what I would expect, purely in the sense that most actual graphing programs aren’t sophisticated enough to be able to do that.
Actually, I turned on complex mode and the four complex roots are plotted on the complex plane, superimposed on top of the equations for the circle on the real plane.
~Max
SageMath isn’t just a graphing program; it is a full featured CAS and general mathematics toolkit using Python as its scripting language; essentially an open source replacemente for Mathematica or Maple. I haven’t used it in years because I do most of my work in NumPy/SciPy/SymPy and various numerical solvers and visualization toolkits in Python, but Sage is quite powerful.
Stranger
I think that, at this point in time, “most graphing programs” is a set that’s made up entirely of TI-84s (which haven’t substantially upgraded their capabilities since 1993, and they weren’t the best even then). And most other standalone graphing calculators, despite being more advanced than the TIs, also can’t do implicit equations.
Desmos is rapidly catching up in market share, though.