Reflection: Connection to Prior Knowledge Dividing Complex Numbers - Section 2: Division of Complex Numbers

 

Emphasize the geometric interpretation!  It's a fact that when the imaginary unit was first proposed, it was derided as just that: imaginary.  It might look good on paper, but it was regarded as essentially meaningless by all of the best mathematicians.

Until, that is, it was given a geometric interpretation.  Once the imaginary unit was understood geometrically, mathematicians were willing to accept it.  Why should our students be any different?  If anything, they have an even greater need for these abstract notions to be given a concrete context!

Be sure to recall for your students the parallelogram rule for adding complex numbers.  This same rule can be applied to the inverse operation: subtraction.  Likewise, once we have a geometric interpretation of multiplication, the same interpretation can be used for the inverse operation.  The factors and the product correspond to three points in the plane, A, B, and C.  The difference between the operations is simply that when multiplying you are given A & B and must find C, but when dividing you are given A & C and must find B.

This geometric interpretation gives meaning to the operation.  Once your students can attach some meaning to it, then you can teach them how to carry it out more efficiently with algebra.

  Thinking Geometrically
  Connection to Prior Knowledge: Thinking Geometrically
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Dividing Complex Numbers

Unit 2: The Complex Number System
Lesson 13 of 16

Objective: SWBAT use the properties of complex conjugates to divide two complex numbers. They will also understand and explain the corresponding graphical representation.

Big Idea: Division of complex numbers is best understood in its relation to multiplication and transformations of the complex plane.

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2 teachers like this lesson
Subject(s):
Math, factoring polynomial expressions, Algebra, Algebra 2, master teacher project, complex numbers, Imaginary Numbers
  45 minutes
complex multiplication image
 
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