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}]