Appendices

Appendix A Complex Numbers

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