Class members perform complex operations on a plane in the 17th segment in the 32-part series. Learners first verify that multiplication by the reciprocal does the same geometrically as it does algebraically. The class then circles back to what they learned in the unit about operations and linear transformations and makes connections between the two.

Concepts

multiplication, complex numbers, reciprocals, complex plane, transformations, rotations, dilation, dilations, inverse, linear algebra

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Additional Tags

math

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Instructional Ideas

• Conduct a quick review on converting polar form to rectangular form
• Use the exploratory challenge two to identify pupils that will need additional review prior to the mid-module assessment

Classroom Considerations

• The class should be familiar with special right triangles and finding sides given another side

Pros

• The scaffolding provides suggestions on how to make the abstractness more concrete for learners that need it
• The exercises ask individuals to summarize what they have learned so far about the geometric representations of the operations on complex numbers

Cons

• None

Common Core

HSN-CN.A.3 HSN-CN.B.4 HSN-CN.B.5 MP2 MP3 MP7