Chapter 14: Properties Of i and Other Complex Numbers: Situation 8 From the MACMTL–CPTM Situations Project

A teacher of an Algebra 3 course noticed that her students often interpreted i in expressions such as 3i,i², and 4i+ 2 as though it were an unknown or variable rather than a number.

This Situation provides different interpretations of the imaginary unit and utilizes the multiplication operation involving this unit. Symbolic, graphical, and geometric representations are used in the set of Foci that follow. Focus 1 treats the imaginary unit as a number that is a solution to a quadratic equation with no real solutions. Focus 2 treats multiplication by the imaginary unit as an operation that rotates points about the origin in the complex plane. Connections are made to vector operations in Focus 3 and Focus 4, and Focus 5 incorporates linear algebra.