I would like to plot the function Arg[z] for a complex number $z$ in three-dimensions: I would like to obtain it as a surface over the complex plane, as in the "3D plot" section of this page:

enter image description here

But I would also like to be able to modify the range and the colors. The function only assumes real values between $-\pi$ and $\pi$.

I found (and tried) Complex3DPlot, but it does not provide what I'm looking for, because it plots the magnitude of Arg[z].

  • 1
    $\begingroup$ Is this what you want? Plot3D[Arg[x + I y], {x, -1, 1}, {y, -1, 1}, ColorFunction -> "Rainbow"] $\endgroup$
    – Domen
    Oct 14, 2021 at 14:24
  • $\begingroup$ @Domen Yes, exactly! Thank you. I had tried something similar and it didn't work, maybe I used a wrong syntax. If you would like to make an answer, it's welcome. $\endgroup$
    – BowPark
    Oct 14, 2021 at 14:26

1 Answer 1


Use Plot3D with $z = x + iy$.

Plot3D[Arg[x + I y], {x, -1, 1}, {y, -1, 1},  ColorFunction -> "Rainbow"]

Mathematica graphics


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