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Number of roots (Rouche Thm)

  1. Sep 18, 2011 #1
    Problem: find number of roots of [itex]z^n + a_{n-1}z^{n-1} + ... + a_0, |z| < 1[/itex]

    What is wrong with this argument:
    Let f(z) = z^n + a_{n-1}z^{n-1} + \cdots + a_0, and g(z) = - a_{n-1}z^{n-1} - ... - a_0. Then, |f| > |g| and f+g = z^n. by Rouche thm, number of roots of f is equal to number of roots of f + g, which is n.
     
  2. jcsd
  3. Sep 22, 2011 #2
    How do you get |f| > |g| ? Try the argument for f(z)=z^2 +2.
     
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