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I first tried to plot a parametric equation as follows; 

ParametricPlot3D[{Zeta[a + b*I]*Cos[Pi*(1 - 2^-(a + b*I))], 
  Zeta[a + b*I]*Sin[Pi*(1 - 2^-(a + b*I))]}, {a, -10, 10}, {b, -10, 10}]

but I am uncertain if it should work or not. I messed around with it a bit but couldn't get it to work, it just returned an empty plot.

Empty plot from the first input

I then went and tried other simpler similar plots, which turned out the same way, such as 

Plot3D[Cos[\[Pi]*(1 - 2^-(a + b*I))], {a, -3, 3}, {b, -3, 3}]

and 

ParametricPlot3D[{Re[Cos[(1 - 2^-(x + 5 I)) π]], Im[Cos[(1 - 2^-(x + 5 I)) π]]}, {x, -1, 1}]

I am not very used to the Wolfram language, so it could just be that.

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  • $\begingroup$ What do you expect to see when the values of the function are complex? $\endgroup$
    – murray
    Commented Jan 14, 2016 at 20:51
  • $\begingroup$ One of your problems is that your function is merely two dimensional, but it should be three-dimensional in ParametricPlot3D. $\endgroup$
    – David G. Stork
    Commented Jan 14, 2016 at 21:24

1 Answer 1

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Perhaps this is the sort of thing you want, shown here for your 2nd example:

Plot3D[ReIm[Cos[\[Pi]*(1 - 2^-(a + b*I))]], {a, -3, 3}, {b, -3, 3}]

enter image description here

Note that function ReIm is new as of Mathematica 10.1. If you're using an earlier version, you'll need to recreate the effect of that, e.g., by means of Through[{Re, Im}[ ....] ].

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