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This paper presents a sequential learning algorithm for a complex-valued resource allocation network with a self-regulating scheme, referred to as complex-valued self-regulating resource allocation network (CSRAN). The self-regulating scheme in CSRAN decides what to learn, when to learn, and how to learn based on the information present in the training samples. CSRAN is a complex-valued radial basis function network with a sech activation function in the hidden layer. The network parameters are updated using a complex-valued extended Kalman filter algorithm. CSRAN starts with no hidden neuron and builds up an appropriate number of hidden neurons, resulting in a compact structure. Performance of the CSRAN is evaluated using a synthetic complex-valued function approximation problem, two real-world applications consisting of a complex quadrature amplitude modulation channel equalization, and an adaptive beam-forming problem. Since complex-valued neural networks are good decision makers, the decision-making ability of the CSRAN is compared with other complex-valued classifiers and the best performing real-valued classifier using two benchmark unbalanced classification problems from UCI machine learning repository. The approximation and classification results show that the CSRAN outperforms other existing complex-valued learning algorithms available in the literature.