Plotting solutions of systems in complex plane

Question

I'm interested in plotting solutions of systems of polynomials in the complex plane, in the following way.

Let $f_1,\ldots f_s$ be complex polynomials in variables $x_1,\ldots x_n$. I know how to find the solutions using a code like this

eqs = {x^2 + y^3 + 1 == 0, x + y^2 - 1 == 0}
pts = Solve[eqs, {x, y}]

But I'm having some trouble to plot the values of $x,y$ n the complex plane. I tried some naive thing like

ListPlot[pts]

but nothing works. I'm lost, any help is welcome, thanks.

I forgot a little detail in my answer, sorry. It's corrected. — Integral, Apr 8, 2015 at 3:21
A math problem: If you have ${x,y}$ as a point and $x$ and $y$ are complex, how does one show them on complex plane? — Mahdi, Apr 8, 2015 at 3:30
$x$ is one point and $y$ is another, their are not considered as coordinates. — Integral, Apr 8, 2015 at 3:33

Mahdi · Accepted Answer · 2015-04-08 03:38:35Z

3

You have

eqs = {x^2 + y^3 + 1 == 0, x + y^2 - 1 == 0};
pts = Solve[eqs, {x, y}];

To get the data points and the plot:

data = {x, y} /. pts // Flatten;
ListPlot[{Re[#], Im[#]} & /@ data]

answered Apr 8, 2015 at 3:21

Mahdi

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$\begingroup$ I think it's perfect! $\endgroup$
– Integral
Apr 8, 2015 at 3:45
$\begingroup$ Do you mind just explain a little (or recommend some reading) what #,&,/ and @ stands for? $\endgroup$
– Integral
Apr 8, 2015 at 3:47
$\begingroup$ Thanks! /@ is shorthand for Map. It basically maps {Re[#], Im[#]} over all elements in data one by one. This page is really good to start! $\endgroup$
– Mahdi
Apr 8, 2015 at 3:53

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ybeltukov · Accepted Answer · 2015-11-21 14:28:55Z

4

Starting from version 10.1 you can use ReIm:

eqs = {x^2 + y^3 + 1 == 0, x + y^2 - 1 == 0};
pts = {x, y} /. Solve[eqs, {x, y}];

ListPlot[ReIm[pts]]

answered Nov 21, 2015 at 14:28

ybeltukov

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$\begingroup$ Or even ListPlot@ReIm@Values@Solve[eqs, {x, y}]. $\endgroup$
– Michael E2
Nov 21, 2015 at 14:35
$\begingroup$ @MichaelE2, hi, please let me know what do you think about this question : mathematica.stackexchange.com/questions/206901/… . Do you think it’s some how related? $\endgroup$
– S.S.
Sep 26, 2019 at 15:10
$\begingroup$ I have Mathematica 9. $\endgroup$
– S.S.
Sep 26, 2019 at 15:12

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2 Answers 2