Complex Numbers in Polar Form; DeMoivre’s Theorem

This Complex Numbers in Polar Form; DeMoivre’s Theorem presentation also includes:

The iconic links between trig functions and complex numbers are introduced in a lesson on the basic properties of complex numbers in polar form. Quickly progressing through the polarization of complex coordinates, a bulk of the worksheet and presentation is spent on the arithmetic of these polar forms. Summaries of instructions for each section keep the class focused on each problem's goal outcome and make this a great worksheet to have in the notes for modeling and review throughout a unit on complex numbers.

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CCSS: Adaptable
Instructional Ideas

  • Link to a world history unit on Protestant-Catholic relations in late seventeenth century Europe, if interested pupils wish to investigate DeMoivre's life and discoveries
  • Play a find-the-point game similar to Battleship! using complex numbers in polar form
  • Consider exploring the similarities of quotient and product rules for logarithms, if taught already  
Classroom Considerations

  • Learners might benefit from having a unit circle handy, with marked sine and cosine values for common angles
  • If calculators are used for trigonometric values, take care that each is in radian mode
  • Presentation makes for a great interactive whiteboard lesson, with steps revealed in turn as the problem is worked
Pros

  • Examples progress logically from basic through more complex
  • Main resource presentation provides step-by-step solutions for each example problem
  • Each worksheet section begins with a summary of notes and procedures for the problems
Cons

  • Additional resources Polar Graphs and Complex Numbers in Polar Form link to unrelated worksheets covering polynomials, natural logarithms, and exponentials
  • Presentation is missing a slide to correspond to the rule for the last problem, finding complex roots