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On the complex plane, I want to plot the set of points defined by the solution of a system of equality and inequalites, such as $S=\{z \in \mathbb{C}| Im[z+1]=0 \cap Re[z+1]>0 \}$. However, ContourPlot does not accept inequalities. Also, RegionPlot do not accept equalities.

Any hints?

Here's a MWE that do NOT work

ContourPlot[Im[Z + 1 /. {Z -> x + I y}] == 0 && Re[Z + 1 /. {Z -> x + I y}] > 0, {x, -2, 2}, {y, -2, 2}]
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1 Answer 1

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Maybe:

ContourPlot[Im[x + I y + 1] == 0, {x, -2, 2}, {y, -2, 2},
 RegionFunction -> Function[{x, y}, Re[x + I y] > 0]]

is what you look for?

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  • $\begingroup$ Except for the wrong inequality, it works. I guess that as a general rule, one should put in ContourPlot the equality and in RegionFunction the solution of the inequalities, something like myFun[Z_] := Z; ContourPlot[Im[myFun[Z] /. {Z -> x + I y}] == 0, {x,-1,1}, {y,-1,1}, RegionFunction -> Function[{x, y}, Re[myFun[Z] /. {Z -> x + I y}] > 0]] $\endgroup$
    – Nicola
    Commented Oct 27, 2014 at 6:27
  • $\begingroup$ Ahh, I missed a 1. I don't know why you are replacing as you do. Why not do myFun[x+I y] directly? $\endgroup$
    – mickep
    Commented Oct 27, 2014 at 6:32
  • $\begingroup$ It depends on your application I guess. $\endgroup$
    – Nicola
    Commented Oct 27, 2014 at 7:36

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