Undergraduates' images of the root concept in ℝ and in ℂ

The study reported in this paper is concerned with undergraduates' images of the root concept with a focus on consistencies and inconsistencies. The data was collected with an online questionnaire from 115 first-year university students. A statistical analysis was applied to capture the variety of students' responses to questions in which square roots were extracted in the field of complex and real numbers, from positive, negative and non-real radicands. A qualitative analysis of students' reasoning revealed the complexity of their concept images, which were compartmentalized into distinct domains and connected with other concepts through schemes. The phenomena of real and complex number biases were indicated.