In this note, we show by counterexamples that some results of Qiu and colleagues [On the restudy of fuzzy complex analysis: Part I. The sequence and series of fuzzy complex numbers and their convergences, Fuzzy Sets and Systems 115 (2000) 445–450; On the restudy of fuzzy complex analysis: Part II. The continuity and differentiation of fuzzy complex functions, Fuzzy Sets and Systems 120 (2001) 517–521.] concerning the convergence of the series of fuzzy complex numbers and the differentiation of fuzzy complex functions are incorrect, and offer some of their modified versions. We also show that the derivative introduced by them is inappropriate for the functions mapping complex numbers into fuzzy complex numbers.