复数辐角的妙用

Wonderful Application of Argument of the Complex Number

利用复数的辐角,不管在初等数学还是在高等数学中,都可以得到一些奇妙的结果;同时,也产生一种很好的方法,比如可以计算出实积分∫π0ecosθcos(nθ-sinθ)dθ的值;也可以处理一类级数∑∞n=1arctan1n2+n+1的收敛性问题.

By using argument of the complex number, some good results emerge in elementary mathemattics and advance mathemattics. At the same time, there are some wonderful methods ,such problem as calculating difinite integral ∫^π _0 e^cosθ cos（nθ-sinθ）dθ ,and discrimnating conver-gence of a type of series ∞^∑_n=1 arctan 1/n^2＋n＋1 ,and so on.