Abstract

This study examined in-service teachers’ understanding of the pure imaginary number ib, particularly in its Cartesian form. This study was part of a broader design-based research study, which involved the development of a professional development (PD) program aimed at exploring five in-service teachers’ understanding of various forms of complex numbers. Data collection included pre- and post-written sessions along with interviews after the PDs. Data pointed to change in teachers’ conceptualization of i where some could not reason algebraically or geometrically initially. Upon completion of the PD, however, all participants identified i as one of the roots of the quadratic equation, x2+1=0 and were able to represent it geometrically as the point (0,1) on the Complex plane. Additionally, all participants recognized the operator interpretation of i as a 90-degree rotation. One participant also noted dilation meaning of b when multiplied with i and another participant reasoned on the repeated addition meaning. The results further highlighted specific challenges teachers faced in conceptualizing the pure imaginary number. Collectively, the results underscore the importance of addressing the pure imaginary part of the Cartesian form and the operator meanings of complex numbers in teacher education. Furthermore, these results suggest that quantitative reasoning could serve as a foundational way of thinking for making sense of complex numbers, including the unit i.

Keywords: Cartesian form of Complex numbers, Teacher knowledge, Quantitative reasoning

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Karagöz Akar, G., Belin, M., Arabacı, N., İmamoğlu Y., & Akoğlu, K. (2025). Teacher’s conceptualizations of different meanings of pure imaginary numbers. Education and Science, 50(223), 199-222. https://doi.org/10.15390/ES.2025.2570