# Plot circle of radio r in complex plane

I am having a brain-not-working day...

Embarrassingly, I can't figure out how to plot a circle on the complex plane with origin z_0 and radio r. Do I just pretend I'm in R^2? Not ideal, since I'd also like to be able to create a table of coordinate points from the circle, too.

Sorry to ask such a basic question. I've got flu and I'm trying to keep myself entertained...

• Please look under Applications for ComplexListPlot. Get well soon.
– Syed
Dec 13, 2022 at 16:22
• I think the simples is to treat the imaginary axes like an real y axis and then use  r = 1; z0 = {1, 1}; ParametricPlot[z0 + r ({1, 0} Sin[phi] + {0, 1} Cos[phi]), {phi, 0, 2 Pi}]  Dec 13, 2022 at 17:55
• I don't think this is a well-formed question. Are you really asking for convenient ways to map back-and-forth between the complex plane and the "regular" cartesian plane? In one direction you have ReIm (as well as Abs and Arg). In the other you can just apply Complex. Dec 13, 2022 at 19:20

z0 = 1 + I;
r = 2;
plot1 = ParametricPlot[ReIm[z0 + r E^(I \[Theta])], {\[Theta], 0, 2 \[Pi]}]


points =
Table[z0 + r E^(I \[Theta]), {\[Theta], 0, 2 \[Pi], \[Pi]/12}]


plot2 = ListPlot[ReIm[points]];
Show[plot1, plot2]


With[{z0 = 1 + 2 I, r = 3},
ComplexContourPlot[
Abs[z - z0] == r, {z, z0 - r (1 + I), z0 + r (1 + I)}]]


With[{z0 = 1 + 2 I, r = 3},
ComplexContourPlot[
Abs[z - z0] == r, {z, z0 - r (1 + I), z0 + r (1 + I)},
MeshFunctions -> {Abs[# - z0] &, Arg[# - z0] &}, Mesh -> {{r}, 20},
MeshStyle -> Directive[Red, AbsolutePointSize[8]]]]