Research on university students ideas about connection between quantum formalism and concepts shows the existence of deep and persistent difficulties but plenty of topics in undergraduate curriculum still await exploration, including basic properties of quantum state representations. A first case study conducted by questionnaire and interview investigated the physical meaning and role ascribed by students to wavefunction (WF) properties. A second pilot study was conducted for the development of an investigation to explore how students link quantum formalism to concepts both in general terms and in the application context of specific problems. We report here the results of the first case study and of the pilot study, for what concerns the complex nature of the WF and quantum state vector. Data analysis of case studies shows how students are focused on the mathematical computational role of the use of complex numbers in quantum mechanics (QM), neglecting physical information encoded in the phase, displaying difficulties in distinguishing information contained respectively in psi and |psi|^2. These results could help explain issues recognized in literature such as using probability amplitude instead of its square modulus to express probability.
