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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 1996 • Question 10

Question

Math 6210 • Real Analysis Fall 1996 • Question 10

Let \(P(z)=kz+z^k\) where \(k\) is a positive integer. Show that \(P\) is one-to-one on \[ \{z:|z|<1\}. \]

Raw LaTeX

Let \(P(z)=kz+z^k\) where \(k\) is a positive integer. Show that \(P\) is
one-to-one on
\[
\{z:|z|<1\}.
\]

Topic Tags

Automorphism Groups and Biholomorphisms