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Complex Product and Quotient Using Similar Triangles
Complex Product and Quotient Using Similar Triangles
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 .
{o,p,a}
{o,b,ab}
{o,p,a}
{o,b/a,b}
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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b
a
b
ab
a b
a b
a
a
b/a
b/a