The paper considers solving problems in information technologies by means of spline approximation and spline extrapolation on the basis of real and complex spline functions. The use of spline approximation based on real quadratic splines to solve the problem of self-similar traffic recovery on the example of voice VoIP traffic is shown. The use of real parametric linear spline functions in the problems of information technologies, namely, the problems of constructing curves and surfaces in 3D modelling, is proposed. It is shown that the use of parametric spline functions in the tasks of reproducing curves and surfaces or approaching the shape of a modelled 3D object allows minimizing the approximation and reproduction errors. To solve the problem of user positioning in the Wi-Fi network, we consider the use of spline approximation based on complex plane spline functions, which allows to improve the accuracy of user positioning in the room. The method of spline extrapolation based on real spline functions is used to detect and predict DDoS cyber attacks. Solving the problem of predicting the characteristics of DDoS cyberattack traffic allows detecting the characteristics of malicious traffic, thereby preventing the destructive consequences of DDoS attacks. It is shown that the use of methods of real and complex spline functions in information technologies allows to obtain results of increasing the accuracy and scalability of the obtained solutions.