In Lessons 8 and 9, students explored the idea that every complex operation must have some geometric interpretation, eventually coming to the realization that complex addition and subtraction have the geometric effect of performing a translation to points in the complex plane.
The geometric interpretation of complex multiplication was left unresolved as students realized it was not readily obvious. Later in the module, students continue to explore the question, “What is the geometric action of multiplication by a complex number 𝑤 on all the points in the complex plane?” To understand this, students first explore the connection between geometry and complex numbers. The coordinate geometry studied in Geometry was about points in the coordinate plane, whereas now the thinking is about complex numbers in the complex plane.
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