Understand the Number i

This Understand the Number i video also includes:

Beginning with a question of when a square number is negative, this short but deep video presentation motivates the creation of the imaginary numbers. Common mistakes in developing the idea of i are carefully addressed, including confusion of the number with a variable and loss of negative signs when squaring. The emphasis on squares and square roots does a great job offering strong math justification for concepts that are often memorized without understanding.

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CCSS: Designed
Instructional Ideas

  • Create a memory-style game where learners match expressions and their verbal expansion, per time-stamp 3:45 on the video
  • Link video on the class website for learners to use for on-demand review while working related homework problems
  • Show during a comprehensive end-of-course review to refresh the theory behind imaginary numbers
Classroom Considerations

  • Viewing the lesson requires creation of a free LearnZillion teacher account
  • Video playing requires updated Adobe Flash player and Internet access
  • Only pure imaginary numbers are covered, not complex numbers with both real and imaginary parts
  • Lesson assumes learners are familiar with rational exponents and the Venn diagram representation of the real number systems and subsystems
  • Printable note slides available under the Additional Materials tab
Pros

  • Clear and easily understood narration, carefully matching text directions
  • Identification and explanation of common areas of confusion
  • Particular care taken with treatment and explanation of how to deal with negative numbers
Cons

  • The imaginary number system is never called the more general and correct complex number system
  • No workable problems or guided practice provided
Common Core