  The complex method to obtain 2-dimensional Born-Infeld electrostatic
solutions is presented in a renewed form. The solutions are generated by a
holomorphic seed that makes contact with the Coulombian complex potential. The
procedure is exemplified by solving the Born-Infeld multipolar configurations.
Besides, it is shown that the attractive force between two equal but opposite
charges is lower than its Coulombian partner; it decreases up to vanish when
the charges approach each other below a distance ruled by the Born-Infeld
constant.
