[试题] 109上 蔡宜洵 复分析导论 第三次小考

楼主: t0444564 (艾利欧)   2020-12-13 11:30:33
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12月03日(四)
考试时限:15:10-15:40,共计30分钟
试题 :
               Complex Analysis
Quiz 3
            Name:         ID:
1. (15 points) Let a1,...,an be points on ∂D(0,1). Prove that there exists a
point z on ∂D(0,1) such that the product of the distances from z to the aj
is at least 1. (Hint: By maximum modulus principle.)
2. (15 points) Let f(z)∈Hol(D(0,1)), f(0) = 1, and Re(f(z)) ≧ 0 for
all z∈D(0,1). Show that
1 - |z| 1 + |z|

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