So my professor threw in what he called an extra 'hard' question for a practice test. So naturally I have a question about it. It relates to the Maximum Modulus Principle:(adsbygoogle = window.adsbygoogle || []).push({});

a) Let [tex]p(z) = a_0 + a_1 z + a_2 z^2 + ...[/tex]

and let M = max |p(z)| on |z|=1.

Show that [tex]|a_i|< M[/tex] for [tex]i = 0,1,2. [/tex]

b) What is the order of the zero at infinity if f(z) is a rational function of the form

[tex]f(z) = \frac {p(z)}{q(z)}[/tex]

where both p(z) and q(z) are both polynomials and [tex] deg(p) < deg(q). [/tex]

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# Homework Help: Complex Analysis question

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