Exploiting the Connection to Cartesian Coordinates

Multiplication in polar form is nice and neat—that is not the case for coordinate representation. Multiplication by a complex number results in a dilation and a rotation in the plane. The formulas to show the dilation and rotation are somewhat unruly. The teacher leads a discussion of needing to have a better notation in the 21st part of the 32-part series.

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CCSS: Designed
Instructional Ideas

  • Review coordinate notation for geometric transformations
  • Begin the lesson by having the class multiply two specific complex numbers and the general case
Classroom Considerations

  • Class members should be comfortable multiplying complex numbers algebraically
Pros

  • The scaffolding gives suggestions on how to reword some of the questions for individuals who may have trouble with them as written
  • The discussion notes foreshadow future lessons, giving learners an idea of upcoming concepts they will cover
Cons

  • None
Common Core