The complex roots of the equation +bz+1=0 are displayed as red dots. The blue dots correspond to the branching points, that is, to such values of that the equation has a double root. The black dot corresponds to , which you can drag to see the roots move. In particular, two roots dance around each other and interchange their positions every time moves around a branching point. So, every time runs in a loop without hitting any branching points, the roots are permuted. The group generated by such permutations is called the monodromy group of the equation. The parameter and the branching points are displayed at a larger scale to keep them well separated from the roots. The green dot shows .
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b=0