Measurements of neutral current cross sections for deep inelastic scattering in e(+)p collisions at HERA with a longitudinally polarized positron beam are presented. The single-differential cross-sections d sigma=dQ(2), d sigma=dx and d sigma=dy and the reduced cross section (sigma) over tilde are measured in the kinematic region Q(2) >185 GeV2 and y and F-3(gamma Z) are determined by combining the e(+)p results presented in this paper with previously published e(-)p neutral current results. The asymmetry parameter A(+) is used to demonstrate the parity violation predicted in electroweak interactions. The measurements are well described by the predictions of the Standard Model.