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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
]



enter image description here



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