A Complex Number Raised to a Complex Exponent: What Does This Mean?. Issue 1 (2nd January 2022) - Palmer, Katrina; Bauldry, William; Bossé, Michael J.; Post, Jaehee
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.