  Using the approach of the splitting method developed by I. Gy\"ongy and N.
Krylov for parabolic quasi linear equations, we study the speed of convergence
for general complex-valued stochastic evolution equations. The approximation is
given in general Sobolev spaces and the model considered here contains both the
parabolic quasi-linear equations under some (non strict) stochastic
parabolicity condition as well as linear Schr\"odinger equations
