比较复变函数与二元函数的分析性质

The Comparison of Analysis Property in Complex Function and the Binary Function

设z=x+iy,w=u+iv,则w=f(z)=u(x,y)+iv(x,y),所以一个复变函数w=f(z)相当于定义两个二元函数u=u(x,y)和v=v(x,y),讨论一个复变函数的极限与连续性就相当于讨论两个二元函数的极限与连续性.所以复变函数与二元函数在某些概念、结论上有一定的相似之处,因此有必要比较复变函数与二元函数的某些分析性质.

Let z=x＋iy,w=u＋iv,then w=f（z）=u（x,y）＋iv（x,y）.Therefore a complex function w=f（z）is equivalent to the definition of the two binary function u=u（x,y）and v=v（x,y）.And the discussion of the limit and continuous property of a complex function,in some degree,is equivalent to the discussion of the same property of two binary function.So,some concepts and properties between them are similar,and there is necessity of comparing some analysis properties of complex function with two binary function.