从复数域的发展过程,谈谈您对数和数学的认识(论文).doc

从复数域的发展过程，谈谈您对数和数学的认识 摘要:域是数学上的一个概念，简单的说就是数的集合，这个集合对加、减、乘、除（分母不为零）四则运算封闭，复数域是由全体复数组成，是特殊的实数域，也是目前发现的最大的一个数域，在数学方面有着很广泛的应用。本论文主要从复数的四则运算，在复平面上的三角形式，在近世代数方面的应用，有关复数域的扩充和在其他领域的应用五个方面来认识数与数学。 关键字：复数 域扩充 应用 Abstract: domain is a concept of mathematics, It a collection of several in brief, this collection of addition, subtraction, multiplication, and division (the denominator is not zero) arithmetic closed, complex domain is composed of all the complex, is a special real domain, also is currently the largest discovery of a number field, has a wide application in mathematics. This thesis mainly from the complex arithmetic, triangle on the complex plane form, the application in modern algebra, complex domain expansion and in other areas of application in five aspects to know Numbers and math. Key word: complex Domain expansion application  目录 摘要..................................................1 引言..................................................3 1.复数的发展过程 .....................................3 2.复数域内复数的四则运算..............................4 2.1复数的加法运算...................................4 2.2复数的减法.......................................4 2.3复数的乘法.......................................4 2.4复数的除法.......................................4 复数域内复数在复平面的三角形式......................5 3.1复平面...........................................5 3.2复数在平面内的表示...............................5 3.3复数的三角形式...................................5 3.3.1复数的三角形式...............................5 3.3.2 非零复数辐角的多值性......................6 　 3.3.3 辐角主值 ....................................6 3.3.4复数三角形式的特点.............6 3.4复数的向量表示...................................7 3.5极坐标形式.......................................9 3.6复数的指数形式...................................10 4.复数域内复数在近世代数中的应用......................11 5.关于复数的扩充......................................11 6.复数域在其他领域的应用..............................15 　6.1拉普拉斯变换.....................................15 6.2根轨迹法........................