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ERIC Number: ED655700
Record Type: Non-Journal
Publication Date: 2023
Pages: 19
Abstractor: As Provided
ISBN: N/A
ISSN: N/A
EISSN: N/A
Available Date: N/A
Different Meanings of Pure Imaginary Numbers
International Society for Technology, Education, and Science, Paper presented at the International Conference on Education in Mathematics, Science and Technology (ICEMST) (Cappadocia, Turkey, May 18-21, 2023)
This study investigated in-service teachers' conceptualization of the pure imaginary number, within the Cartesian form, "a" + "ib" where "a" and "b" are real numbers and "i" is the imaginary unit. As part of a larger design-based research study, in which a professional development (PD) program was designed to investigate five in-service teachers' conceptualization of different forms of complex numbers, we conducted pre and post written problem-solving sessions together with post PD interviews. Results showed that after PD all the participants defined "i" as one of the roots of the quadratic equation, x[superscript 2] + 1 = 0. They also could show geometrically as a point (0,1) on the complex plane. Although all the participants mentioned operator meaning of "i" as a 90-degree rotation when multiplied with b; only one of them mentioned the dilation meaning of b when multiplied with "i". Results suggested considering the pure imaginary part of the Cartesian form focusing on both the operator meanings of b and "i" is important for understanding the nature of complex numbers and the complex plane for teacher education and teacher content knowledge. These results further suggest that quantitative reasoning might lay a foundation for connecting different forms of complex numbers, including the unit, "i." [For the complete proceedings, see ED655360.]
International Society for Technology, Education, and Science. 944 Maysey Drive, San Antonio, TX 78227. Tel: 515-294-1075; Fax: 515-294-1003; email: istesoffice@gmail.com; Web site: http://www.istes.org
Publication Type: Speeches/Meeting Papers; Reports - Research
Education Level: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: N/A