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Introduction to Abstract Algebra, 4th Edition by W. Keith Nicholson

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Appendices

Appendix A Complex Numbers

The set img of real numbers has deficiencies. For example, the equation x2 + 1 = 0 has no real root; that is, no real number u exists such that u2 + 1 = 0. This type of problem also exists for the set img of natural numbers. It contains no solution of the equation x + 1 = 0, and the set img of integers was invented to solve such equations. But img is also inadequate (for example, 2x − 1 = 0 has no root in img), and hence the set img of rational numbers was invented. Again, img contains no solution to x2 − 2 = 0, so the set img of real numbers was created. Similarly, the set img of complex ...

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