[Math] What online graphing tools handle complex numbers well

Question

What online graphing tools handle complex numbers well?

Desmos is generally excellent by breaking functions down into their real and imaginary parts and plotting on the Euclidean plane. For example it can relatively easily graph:

$f:\Bbb N\to\Bbb C$

$f(x)=x\cdot\exp{(2\pi i\log_{\frac23}x)}$

as shown here, and it displays and prints nicely.

But I want to plot $f(x)=x\cdot\exp{(2\pi i\log_{\frac{-1}3}x)}$ which is a little more tricky as it requires the imaginary unit within the exponent because $\log(-1/3)=i\pi-\log(3)$

Is there a way with desmos, or an easy-to-use alternative tool?

Answer 1

You can try WolframCloud, it is Mathematica with some limitations (computing time, ...)

f[x_]:= x Exp[2 Pi  I  Log[-1/3,x]];
t = Table[{Re[f[x]],Im[f[x]]},{x,1,10}];
ListPlot[t, Joined->True]

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EDIT

To include labels you can use something like this

f[x_]:= x Exp[2 Pi  I  Log[-1/3,x]];
t = Table[{Re[f[x]],Im[f[x]]},{x,1,10}];
ListLinePlot[t->Range[10], PlotMarkers -> {Automatic, 10},LabelingFunction->Left]