In this paper, we present two fast learning neural network classifiers with a single hidden layer: the 'Phase Encoded Complex-valued Extreme Learning Machine (PE-CELM)' and the 'Bilinear Branch-cut Complex-valued Extreme Learning Machine (BB-CELM)'. The proposed classifiers use the phase encoded transformation and the bilinear transformation with a branch-cut at 2π as the activation functions in the input layer to map the real-valued features to the complex domain. The neurons in the hidden layer employ the fully complex-valued activation function of the type of a hyperbolic secant function. The parameters of the hidden layer are chosen randomly and the output weights are estimated as the minimum norm least square solution to a set of linear equations. The classification ability of these classifiers are evaluated using a set of benchmark data sets from the UCI machine learning repository. Results highlight the superior classification ability of these classifiers with least computational effort.