Bôcher's theorem

In complex analysis, the theorem states that the finite zeros of the derivative ${\displaystyle r'(z)}$ of a nonconstant rational function ${\displaystyle r(z)}$ that are not multiple zeros are also the positions of equilibrium in the field of force due to particles of positive mass at the zeros of ${\displaystyle r(z)}$ and particles of negative mass at the poles of ${\displaystyle r(z)}$, with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.
Furthermore, if C1 and C2 are two disjoint circular regions which contain respectively all the zeros and all the poles of ${\displaystyle r(z)}$, then C1 and C2 also contain all the critical points of ${\displaystyle r(z)}$.