课程名称︰复分析导论
课程性质︰数学系大三必修
课程教师︰蔡宜洵
开课学院：理学院
开课系所︰数学系
考试日期︰2020年11月12日(四)
考试时限：13:20-15:10，共计110分钟，最后加五分钟。
试题 :
　　　　　　　　　　　　　　　Complex Analysis
　　　　　　　　　　　　　　　 November 12, 2020
　Total points: 105
Note. 1) Your arguments and calculation details must be clear and complete;
the auxiliary theorems needed for any claim of your results must be
explicitly indicated. Failing to do so may result in loss of partial or
full points.
1. Let D be the open disk, centered at 0, of radius r.
r
z 2020 n
　 i) (15 points) Use Rocuhe theorem to show that the equation e - e z = 0
has exactly n roots (counted with multiplicity) in D .
1
ii)(10 points) Replace D by D and ask for D which encloses all the above
1 r r
n roots. Find the smallest r that can be obtained by your method in i).
+∞ e^(ax)
2. (20 points) Compute ∫