A Complex Number Raised to a Complex Exponent: What Does This Mean?. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Palmer, Katrina; Bauldry, William; Bossé, Michael J.; Post, Jaehee
• Is Part Of: PRIMUS. Volume 32:Issue 1(2022)
• Page Start: 106
• Page End: 115
• Publication Date: 2022-01-02
• Subjects: Complex numbers -- exponents -- number systems; Mathematics -- Study and teaching (Higher) -- Periodicals; 510.711
• DOI: 10.1080/10511970.2020.1827328
• Languages: English
• ISSNs: 1051-1970

Abstract

ABSTRACT: Most any students can explain the meaning of a b, for a ∈ R and for b ∈ Z . And some students may be able to explain the meaning of ( a + b i ) c, for a, b ∈ R and for c ∈ Z . However, few may be able to explain a d i or a ( c + d i ) let alone ( a + b i ) ( c + d i ) for a, b, c, d ∈ R . Through both mathematical explanation and reader investigations via a dynamic graphing applet, we will investigate the meaning of ( a + b i ) ( c + d i ) . Additionally, we provide some course-appropriate investigations which can be used by instructors in various grades 11–16 courses.