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10. The complex numbers, the Fundamental Theorem of Algebra and polynomial equations
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Benjamin Fine
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Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- 1. The natural, integral and rational numbers 1
- 2. Division and factorization in the integers 19
- 3. Modular arithmetic 39
- 4. Exceptional numbers 61
- 5. Pythagorean triples and sums of squares 83
- 6. Polynomials and unique factorization 95
- 7. Field extensions and splitting fields 125
- 8. Permutations and symmetric polynomials 141
- 9. Real numbers 157
- 10. The complex numbers, the Fundamental Theorem of Algebra and polynomial equations 189
- 11. Quadratic number fields and Pell’s equation 227
- 12. Transcendental numbers and the numbers e and π 249
- 13. Compass and straightedge constructions and the classical problems 289
- 14. Euclidean vector spaces 303
- Bibliography 327
- Index 329
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- 1. The natural, integral and rational numbers 1
- 2. Division and factorization in the integers 19
- 3. Modular arithmetic 39
- 4. Exceptional numbers 61
- 5. Pythagorean triples and sums of squares 83
- 6. Polynomials and unique factorization 95
- 7. Field extensions and splitting fields 125
- 8. Permutations and symmetric polynomials 141
- 9. Real numbers 157
- 10. The complex numbers, the Fundamental Theorem of Algebra and polynomial equations 189
- 11. Quadratic number fields and Pell’s equation 227
- 12. Transcendental numbers and the numbers e and π 249
- 13. Compass and straightedge constructions and the classical problems 289
- 14. Euclidean vector spaces 303
- Bibliography 327
- Index 329
