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f(x)=square(X)+ix. Plot a 3D plane for this complex function

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    $\begingroup$ What is the relation of "a 3D plane" to this equation??? $\endgroup$ Jan 31, 2023 at 2:35
  • $\begingroup$ What is a 3D plane? I've always thought that a plane can only be 2D. $\endgroup$
    – yarchik
    Jan 31, 2023 at 11:17

2 Answers 2

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You could take the real part of $f$ as the $x$ coordinate, the imaginary part of $f$ as the $y$ coordinate, then use either the Abs of $f$ or its Argument for the $z$ coordinate and use ParametricPlot3D

f[z_] := Sqrt[z] + I*z;
ParametricPlot3D[{Re[f[x + I*y]], Im[f[x + I*y]], 
  Abs[f[x + I*y]]}, {x, -5, 5}, {y, -5, 5}, 
 AxesLabel -> {"Real part", "imaginary part", "Magnitude"}]

Mathematica graphics

ParametricPlot3D[{Re[f[x + I*y]], Im[f[x + I*y]], 
  Arg[f[x + I*y]]}, {x, -5, 5}, {y, -5, 5}, 
 AxesLabel -> {"Real part", "imaginary part", "Phase"}, 
 PlotRange -> All]

Mathematica graphics

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f[z_] := z^2 + I*z

ComplexPlot3D[f[z], {z, -5 - 5 I, 5 + 5 I},
 AxesLabel -> {Re[z], Im[z], Abs[f[z]]},
 Mesh -> Automatic,
 PlotPoints -> 100,
 MaxRecursion -> 4,
 PlotLegends -> BarLegend[Automatic,
   LegendLabel -> Arg[f[z]]]]

enter image description here

ParametricPlot3D[
 {Re[f[z]], Im[f[z]], z},
 {z, -5, 5},
 AxesLabel ->
  {HoldForm@Re[f[z]], HoldForm@Im[f[z]], z}]

enter image description here

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