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

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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