In this paper the problem of single-stage vapor-liquid flash calculations using equations of state is addressed. A solution scheme in the framework of complex domain is used in conjunction with a Newton-based formulation in block algebra, providing an efficient, robust, and reliable computation scheme. The new scheme minimizes the number of iterations, because it always ensures a direct-forward step toward the solution, making fewer calls to thermodynamic property evaluations during iterations and avoiding the use of pseudophases along the calculation path. Convergence to unambiguous results is assured for all cases of practical interest, because derivative discontinuities inherent to real-domain models, including the need for bounding mole fractions to lie between 0 and 1, are avoided. The efficiency and robustness of the proposed scheme are shown by calculations in the retrograde region and in the construction of phase envelopes for model mixtures.