MATH253 Chapter Notes - Chapter 1-24: Quadratic Equation, International Polar Year
18 Jun 2015
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Math 311 lec a1 - spring 2015; fill in for the class lectures. Theory of functions of a complex variable, adapted from james lewis"s informal lecture notes. Consider the equations x 1 0. The rst equation invented the negative integers t 1, 2, u and the negative real numbers. Nowadays, negative real numbers are somewhat second nature. The second equation has no real solution since x2 0 for all real numbers x. The invented solution here, denoted by i, is a choice of ? 1". Thus (more correctly) i2 1 and it solves the second equation. Obviously since i is not real implies that we have to extend our number system into complex numbers. To a mathematician, complex numbers are second nature ! N denotes the set of natural numbers, z denotes the set of integers, r denotes the set of real numbers and.
