Geometry: An Interactive Journey to Mastery

Complex Numbers in Geometry

Lesson 35

Topics
x Introduction to complex numbers.
x The geometric effect of multiplication by i.
x Applications to geometric problems.
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x complex number: A number of the form a + ib, with a and b each a real number and i an alleged
quantity with the mathematical property that i^2  í
x median of a triangle: A line segment that connects one vertex of a triangle to the midpoint of its
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Result
x If a point P ͼ௘a, b௘ͽLVUHSUHVHQWHGDVDFRPSOH[QXPEHUa + ibWKHQ³iP ́ iͼ௘a + ib௘ͽ íb + ia
represents the point P rotated about the origin counterclockwise through an angle of 90°.
Summary
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thereby be able to perform arithmetic on them. This provides a powerful new approach to proving geometric
results. In this lesson, we introduce complex numbers, discuss their arithmetic, and explore some applications
of their might.