TRANSFORMATION GEOMETRY USING COMPLEX NUMBERS
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Date
2010-06
Authors
TANG, LEE ROON
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Abstract
Transformation geometry is one ofthe importance modem mathematics. It is basic to
most of the engineering mathematics. There are several transformations, i.e.,
reflection, rotation, translation, dilation, inversion etc. All these transformations will
explain more detail in this project.
The main objective of this project is to explore transformation geometry using
complex numbers. We will go through the transformation geometry which involve
the basic algebraic of complex numbers such as addition, subtraction, multiplication
and conjugation. In geometrically, the transformation geometry of addition or
subtraction of two complex numbers is translation, multiplication with a real number
to the complex number is dilation, multiplication of two complex numbers is a
rotation, and conjugation of complex number is reflection.
The most interesting part at this project is about the inversion geometry. We will
explore the images of the inversion of straight line and inversion of circles for the
transformation of ~ . Furthermore, we will explore to the images of inversion for the
transformation of ~ + z too.
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Keywords
GEOMETRY , NUMBERS