plotting - Is there a simple way to plot complex numbers satisfying a given criteria

I think this should be straightforward, but I cannot seem to find a good source on how to do it after searching around, so

I'm trying to sketch sets of complex numbers that meet a given for criteria. For inequalities, I can get a sketch using RegionPlot. For instance, I can obtain the inequality $|z| < 1$ by

RegionPlot[Abs[z]<1,{x,-1.5,1.5},{y,-1.5,1.5}]

However, given the equality $z + \bar{z} = |z|^2$ I cannot seem to figure out how to get Mathematica to sketch the set of point in the complex plane meeting that criteria. Is there a simple way to accomplish this? (I'm self-studying a complex analysis book that has a bunch of these exercises, and I'd like to just quickly visualize what's going on in all the examples.) Thanks in advance for your help.

Answer

Use ContourPlot for equalities:

ContourPlot[
    Evaluate[z + Conjugate[z] == Abs[z]^2 /. z -> x + I y],
    {x, -2, 2},
    {y, -2, 2},
    FrameLabel -> Automatic
]

Comments

plotting - Filling between two spheres in SphericalPlot3D

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plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Adding a thick curve to a regionplot

Suppose we have the following simple RegionPlot: f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}] Now I'm trying to change the curve defined by $y=g[x]$ into a thick black curve, while leaving all other boundaries in the plot unchanged. I've tried adding the region $y=g[x]$ and playing with the plotstyle, which didn't work, and I've tried BoundaryStyle, which changed all the boundaries in the plot. Now I'm kinda out of ideas... Any help would be appreciated! Answer With f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 You can use Epilog to add the thick line: RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}, PlotPoints -> 50, Epilog -> (Plot[g[x], {x, 0, 2}, PlotStyle -> {Black, Thick}][[1]]), PlotStyle -> {Directive[Yellow, Opacity[0.4]], Directive[Pink, Opacity[0.4]],

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