Im experimenting with different computer algebra systems trying to plot a function of the kind

$$f:\Bbb R\to\Bbb C$$

in 3D, but I dont know a simple and direct solution in any CAS to this kind of plot. To context the question I will leave an elementary function and I will be glad to see some example, the simpler and direct the best, to plot it in 3d in any CAS.

Let $f:\Bbb R\to\Bbb C$ such that $x\mapsto i^x$

My interest is mainly in free software like Sage, Sympy, Maxima or Axiom. I tried too Geogebra but it doesnt support in any way complex numbers so I cant plot the above in any direct way.

Thank you in advance.


2 Answers 2


While Mathematica is not free you can use it for free via Wolfram's Open Programming Lab - https://lab.open.wolframcloud.com/

Here is my go at your graph using it: enter image description here

  • $\begingroup$ Ah, thank you, I dont knew this wolframcloud, seems an intermediate solution between paid software and completely free one. $\endgroup$
    – Masacroso
    Oct 27, 2016 at 16:54
  • $\begingroup$ It has some limitations compared to full Mathematica but from my experience these are generally around limiting the time/amount of computations. So if you aren't doing hundreds of these types of graphs you should be fine. $\endgroup$
    – Ian Miller
    Oct 27, 2016 at 16:57
  • $\begingroup$ Well, I see that the same "trick" of parametric plot work for sage. $\endgroup$
    – Masacroso
    Oct 27, 2016 at 17:24
  • 1
    $\begingroup$ Can you post that "trick" in Sage as an answer or update? $\endgroup$
    – kcrisman
    Oct 27, 2016 at 18:01

The best solution I found by now is a parametric plot in Geogebra, unexpectedly expressions like $\Re(i^x)$ and $\Im(i^x)$ works inside of parametric curves in geogebra.

Then the code

Curve[u, real(ί^u), imaginary(ί^u), u, -10, 10]

works perfectly. You can check it here.


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