Plot complex numbers in the complex number field

Questions
1

Hi,
I’m using Mathematica 10 and want to plot a list of complex numbers in the complex number field and simply don’t succeed to.
ListPlot is not working, ComplexListPlot is not available yet, ReIm not anymore.
The application is to read out the complex numbers from a text file and plot them.
My code so far:

FileData = Import["File.txt"];
Pole = ToExpression[StringSplit[FileData, "\n"], StandardForm];

Any help is highly appreciated,
Richard

2

Moderators’ note for the readers: The following thread was suggested for the author of this question before:
https://mathematica.stackexchange.com/questions/7275/how-can-i-generate-this-domain-coloring-plot

3

Can you provide a sample of Pole?

4

Hello Rohit,
thanks for your reply.

Pole = {1,-1-I,-1+I}

after import and split. Three little complex numbers. Nothing more.
The final graphic should be looking similar to this:

graphic_template.png
graphic_template.png508×401 3.4 KB

5

Hi Richard,

ComplexListPlot was added in V12.

ComplexListPlot[{1, -1 - I, -1 + I}, PlotTheme -> "Detailed", PlotMarkers -> "OpenMarkers"]

4215plot.png
4215plot.png450×468 3.17 KB

6

Thanks, Rohit!
I knew about ComplexListPlot in V12 already, but I’m honestly surprised that there is no simply solution in earlier versions. (Maybe in an add-on?)
Thanks again!

7

Simple solution for earlier versions

ListPlot[ReIm@{1, -1 - I, -1 + I},
 PlotTheme -> "Detailed",
 PlotMarkers -> "OpenMarkers",
 AspectRatio -> Automatic]
8

My installation doesn’t recognize the command ReIm.
The help window gives me the info:
“AlgebraReIm was available as an add-on package in previous versions of Mathematica and is now available on the web at Wolfram Library Archive--Resources and References for Mathematica and Other Wolfram Products”
The m-file that I can download under this link contains the text:

(* ::Package:: *)
(* :Title: ReIm *)
(* :Summary:
The ReIm package is obsolete. Use instead functionality
provided by Assuming, Assumptions, ComplexExpand, Refine,
and similar functions.
*)
(* :Copyright: Copyright 1990-2007, Wolfram Research, Inc.  *)
Message[General::obspkg,"Algebra`ReIm`"];
BeginPackage["Algebra`ReIm`"]
(*ReIm::obslt =
"The ReIm package is obsolete. Use instead functionality provided by \
Assuming, ComplexExpand, Refine, and similar functions.";*)
EndPackage[]

Seems that ReIm is too old.
I tried (and tried to understand) the mentioned commands but none worked.

9

Re and Im have been in WL since V1.

ListPlot[{Re@#, Im@#} & /@ {1, -1 - I, -1 + I},
 PlotTheme -> "Detailed",
 PlotMarkers -> "OpenMarkers",
 AspectRatio -> Automatic]
10

That works.
Thanks again a lot, I owe you one!