Technologically Embodied
Geometric Functions
Complex Multiplication Part 5: Simplify the Complex

Return to the complex multiplication overview.

In this activity you will explore some additional interesting questions about how complex multiplication works.

  1. Page 1: You will review the similar-triangle construction that helps to justify the dilate-rotate method of multiplying complex numbers.
  2. Page 2: You'll do the similar-triangle construction again, but this time without all the other construction lines.
  3. Page 3: Complex multiplication made simple! Just dilate-rotate one of the vectors using the polar coordinates of the other as `s` and `phi`.
  4. Page 4: Is complex multiplication commutative? Does `v*w = w*v`?
  5. Page 5: Is the dilate-rotate composition commutative? Does dilate-rotate give the same result as rotate-dilate?
  6. Page 6: Experiment on your own! What if the vectors are attached to the real axis? to the imaginary axis? What other investigations can you try?

 
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Update History:

18 October 2016: Created this page.