Problem: find number of roots of [itex]z^n + a_{n-1}z^{n-1} + ... + a_0, |z| < 1[/itex](adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Number of roots (Rouche Thm)

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