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Complex Product and Quotient Using Similar Triangles

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Two similar triangles can be used to construct the product of two complex numbers. The triangle with vertices is similar to the triangle with vertices . Similarly (pun intended), quotients can also be constructed by noticing that the triangle with vertices is similar to the triangle with vertices .

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By dragging the locators at and , a series of questions can be tackled in the classroom. For instance, when are , and collinear? When is a real number? When is an imaginary number (with real part zero)? What happens if is a real number? What happens if is imaginary? When is a real number? When is an imaginary number?

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Contributed by: Jaime Rangel-Mondragon (July 2011)
Open content licensed under CC BY-NC-SA

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