Research goals: to determine the ways of differentiation of future mathematics teacher learning to complex analysis using CoCalc. Research objectives: to analyze the problem of differentiating learning in pedagogical universities, particularly in process of teaching the professional disciplines; to determine the place of complex analysis in mathematical disciplines of pedagogical universities; to investigate the impact of CoCalc on differentiation of future mathematics teachers learning to complex analysis. Object of research: learning to complex analysis of future mathematics teachers at pedagogical universities. Subject of research: differentiation of student learning to complex analysis. Research methods used: analysis of scientific publications, observations, interviews with teachers. Results of the research. Based on the analysis of scientific works and interviews with teachers established that the problem of differentiating learning is very relevant during teaching of mathematical disciplines. Defined the place of complex analysis in mathematical disciplines. It’s shown that differentiated instruction is intended to include differentiated tasks in the learning. The specificity using CoCalc on “Complex function of complex variable” are described. The main conclusions and recommendations: 1) expedient use of differentiated tasks (which are distributed by different criteria) as a basic premise differentiation of education; 2) gradual complication of tasks with the gradual generalization of already learned material research and comprehension level.