Exploring Grade XI Students’ Pattern Recognition in Solving Complex Number Exponentiation Problems: A Qualitative Study
DOI:
https://doi.org/10.61255/jupiter.v4i3.1136Keywords:
Complex Number Exponentiation, Mathematical Reasoning, Pattern RecognitionAbstract
Purpose – This study aims to explain students' ability to recognize patterns (pattern recognition) when solving complex number exponentiation problems, especially in shapes with great rank. The focus of the research is directed at how students identify cyclic patterns and use those structures to simplify calculations. Methods – This study employed a descriptive qualitative approach involving three Grade XI students selected through purposive sampling. Data were collected through problem-solving tests, students’ written work documentation, controlled think-aloud protocols, and semi-structured interviews. The data were analyzed using interactive qualitative analysis consisting of data reduction, data display, and conclusion drawing to identify students’ pattern recognition processes in solving complex number exponentiation problems. Findings – The findings revealed that all participants successfully recognized the cyclic power pattern of the imaginary unit , namely and , which repeats every four powers. Students used this cyclic structure together with modulo 4 reasoning to simplify high-order exponentiation problems, such as determining the value of and simplifying expressions involving . Although the participants employed different solution strategies, all were able to identify the same underlying mathematical structure and arrive at correct solutions. These results indicate that pattern recognition plays a central role in supporting students’ mathematical reasoning and efficient problem-solving in complex number exponentiation. Research implications – These findings indicate that learning mathematics in complex number materials needs to emphasize the development of pattern recognition skills so that students can more easily understand abstract concepts and reduce computational burden. Originality – This research makes a new contribution by highlighting specifically how complex number cyclic patterns are used by students to solve large ranks, as well as mapping the variation of strategies that arise in the mathematical reasoning process.
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