Imaginary Numbers Are Real (Part 3: Cardan's Problem)

Were complex numbers discovered or invented? A video presentation makes the case for the discovery of square roots of negative one. In order for complex numbers to be real, then they must behave like other numbers, which they do in terms of the ability to split up and to follow algebra rules. 

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CCSS: Adaptable
Instructional Ideas

  • Use the ability to split apart square roots of negative numbers to simplify numerical expressions containing square roots of negative numbers
  • Have pairs verify that the algebra rules for working with square root of negative one are the same as they are for working with x
Classroom Considerations

  • The third video in a nine-part series
Pros

  • Provides the beginning conceptual understanding for operations with complex numbers
  • Short and engaging supplment to a discussion on the history of imaginary numbers
Cons

  • None