Abstract
The field of complex numbers can be an exciting new topic for students to explore. A class can help discover some motivation for that inscrutable definition for multiplying complex numbers. The trend now seems to be for authors to introduce complex numbers as ordered pairs of real numbers, but the potential for any student participation in this exploration is usually quickly destroyed by the introduction of that mysterious, difficult, and totally unmotivated rule for multiplying these new numbers. It takes the students a while to memorize a definition that they do not understand. But then checking the field properties is as easy as it is boring! What can teachers do to avoid this trap? Why not let the class help in the pursuit of an acceptable definition for the operation of multiplication on these ordered pairs?
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