What online graphing tools handle complex numbers well?

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?

• Your $log_b$ function with a negative base $b$ is uncommon, I would even say not acceptable as such. No surprise that this software doesn't find it sympathetical... May 16, 2019 at 10:34
• Wolfram Alpha is my favorite ! May 16, 2019 at 10:59
• @Peter are you able to plot the points of $f:\Bbb N\to\Bbb C, f(x)=x\cdot\exp{(2\pi i\log_{\frac23}x)}$ in Wolfram Alpha like here desmos.com/calculator/w1ngrpm43z? I use Wolfram lots but always use Desmos because I've never been able or known how to plot those points in Wolfram Alpha. e.g. how do you give it a list of integers? May 16, 2019 at 11:03
• @user334732 I am pretty sure there is a way, but I did not try much in this direction. But other users of Wolfram Alpha should be on this site. Someone might know how it works. May 16, 2019 at 11:06
• Does this answer your question? What free tools can I use to plot complex functions on the complex plane? Apr 3, 2022 at 17:34

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]


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]


• Thanks. Can you get it to look like this: desmos.com/calculator/w1ngrpm43z ? I can already graph what you show with wolfram. May 16, 2019 at 11:04
• @user334732 Like this? May 16, 2019 at 11:10
• Are you seeing a spiral in the complex plane when you click on the Desmos link, with each point plotted labelled with its associated odd number? May 16, 2019 at 11:23
• That script does actually look right, just the graph doesn't look how I expected! Is it possible to label the points too? I'll investigate further based on this. May 16, 2019 at 13:32
• @user334732 Added an edit May 16, 2019 at 13:37