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2
2.
2.
2.2.2.2.
2.
2.2.ContentsGeometric Representation of the Operations with Complex
Numbers
Exercises 1.
Powers of Complex Numbers
Extraction of Roots ,
Exercises 1.
Powers with Fractional Exponents
Powers with Base e and a Complex Exponent
Logarithms to the Base e
Powers with a Complex Base and a Complex Exponent
Exercises 1. 6
Infinity in the Complex Plane. The Riemann Sphere
Exercises 1. 7
The General Binary Complex Number
Hypercomplex Numbers. Quaternions
Axiomatic Foundation of the Complex Number System
BibliographyTopology of Plane Sets of Points
Introduction
Some Additional Definitions
The Calculus of Sets. Boolean Algebra
Exercises 2.
Sets of Complex Numbers
Exercises 2.
Metric Spaces
Exercises 2.
Neighborhoods. Open and Closed Sets
Sets Associated with a Given Set
Isolated Points, Limit Points, and Contact Points. Derived
Set. Dense and Perfect Sets
Distance from a Point to a Set and Distance Between Two
Sets. Diameter of a Set, Bounded Sets
Exercises 2.
Connected Sets
Exercises 2.
· Compact Sets
Exercises 2.
Completeness
Exercises 2. 7
Topological Spaces35
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