It is shown that n points and e lines in the complex Euclidean plane
C2 determine O(n2/3e2/3+n+e) point-line incidences. This
bound is the best possible, and it generalizes the celebrated theorem by
Szemer\'edi and Trotter about point-line incidences in the real Euclidean plane
R2.Comment: 24 pages, 5 figures, to appear in Combinatoric