Discovering the Geometric Effect of Complex Multiplication

Does complex number multiplication have the class spinning? Here's a resource that helps pupils explore and discover the geometric effect of multiplying complex numbers. In the 14th installment in the 32-part unit groups look at the unit square and what happens when the vertices are multiplied by a complex number. Individuals then discover the dilation factor and the rotation angle and how they relate to the modulus and argument of the complex number.

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CCSS: Designed
Instructional Ideas

  • Use geometry software to show the transformations on the unit square
Classroom Considerations

  • The class should be familiar with finding the modulus and argument of complex numbers
  • The resource is an exploratory lesson; allow the class to explore the effects instead of simply telling them
Pros

  • The teacher notes provide questions to ask the class during the discussion portions of the lesson
  • The problem set revisits the idea of linear transformations in context of complex number multiplication
Cons

  • None
Common Core