Error Analysis in Third-Year Complex Number Topics
A Study of Undergraduate Mathematics Students in a Nigerian University
DOI:
https://doi.org/10.53449/zc1hpz13Keywords:
complex numbers, De Moivre's theorem, error analysis, students' difficulties, undergraduate mathematicsAbstract
This study investigates error patterns made by undergraduate mathematics education students at a Nigerian university when solving problems on third-year complex number topics. Eighteen third-year students enrolled in MATH307 (Complex Analysis I) participated in the study. Participants attempted six open-ended tasks covering algebraic simplification, the complex conjugate, division, multiplication, modulus and argument of a complex quotient, and the application of De Moivre's theorem. Their handwritten responses were analysed using a four-category error taxonomy: Conceptual, Interpretation, Procedural, and Technical. Findings reveal that all four error types were present across the six tasks, with Conceptual errors being the most frequent (n = 26), driven largely by near-total failure on the De Moivre's theorem task (12 of 18 students). Interpretation errors (n = 17) exhibited a consistent cross-task pattern: students systematically substituted modulus-argument or polar-form procedures for tasks requiring simpler operations, reflecting overgeneralization of a recently acquired schema. Procedural errors (n = 7) were concentrated in multiplication and division tasks, while Technical errors (n = 3) involved arithmetic lapses in otherwise structurally correct solutions. A key cross-task finding is the cumulative dependency of errors: students who could not divide complex numbers in Question 3 were subsequently unable to simplify the quotient required by Question 5. These findings carry specific implications for the sequencing and emphasis of instruction in complex number courses.
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Copyright (c) 2026 Gafari Lukumon, Kafilat Adebimpe Salahudeen, Philip Iyiola Farayola, Adeniyi Musibau Gbolagade, Tajudeen Motunrayo Asiru, Sunday Oloruntoyin Sangoniyi, Ebenezer Esenogho, Aneshkumar Maharaj
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