Introduction to the Geometry of Complex Numbers

Overview


Geared toward readers unfamiliar with complex numbers, this text explains how to solve the kinds of problems that frequently arise in the applied sciences, especially electrical studies. To assure an easy and complete understanding, it develops topics from the beginning, with emphasis on constructions related to algebraic operations.
The three-part treatment begins with geometric representations of complex numbers and proceeds to an in-depth survey of elements of analytic ...
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Introduction to the Geometry of Complex Numbers

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Overview


Geared toward readers unfamiliar with complex numbers, this text explains how to solve the kinds of problems that frequently arise in the applied sciences, especially electrical studies. To assure an easy and complete understanding, it develops topics from the beginning, with emphasis on constructions related to algebraic operations.
The three-part treatment begins with geometric representations of complex numbers and proceeds to an in-depth survey of elements of analytic geometry. Readers are assured of a variety of perspectives, which include references to algebra, to the classical notions of analytic geometry, to modern plane geometry, and to results furnished by kinematics. The third chapter, on circular transformations, revives in a slightly modified form the essentials of the projective geometry of real binary forms. Numerous exercises appear throughout the text.
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Product Details

  • ISBN-13: 9780486466293
  • Publisher: Dover Publications
  • Publication date: 3/5/2008
  • Series: Dover Books on Mathematics Series
  • Pages: 208
  • Product dimensions: 5.50 (w) x 8.45 (h) x 0.41 (d)

Table of Contents


I. Geometric Representation of Complex Numbers
1. Fundamental Operations
2. Fundamental Transformations
3. Anharmonic Ratio
II. Elements of Analytic Geometry in Complex Numbers
1. Generalities
2. Straight Line
3. The Circle
4. The Ellipse
5. Cycloidal Curves
6. Unicursal Curves
7. Conics
8. Unicursal Bicircular Quartics and Unicursal Circular Cubics
III. Circular Transformations
1. General Properties of the Homography
2. The Similitude Group
3. Non-similitude Homography
4. Möbius Involution
5. Permutable Homographies
6. Antigraphy
7. Product of Symmetries
Index
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