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If the limit as |z| approaches infinity implies |P(z)| approaches infinity for some non-constant polynomial then there exists an a in C such that |P(a)| <or= |P(z)| for all z. Why does this follow?

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- Thread starter moo5003
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- #1

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If the limit as |z| approaches infinity implies |P(z)| approaches infinity for some non-constant polynomial then there exists an a in C such that |P(a)| <or= |P(z)| for all z. Why does this follow?

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JasonRox

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If the limit as |z| approaches infinity implies |P(z)| approaches infinity for some non-constant polynomial then there exists an a in C such that |P(a)| <or= |P(z)| for all z. Why does this follow?

I don't quite remember exactly how it goes, but I remember it using 1/|P(z)|.

I'd have to wait until I get home to find out how it went.

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Note: z_0 is on interior of the disk not the boundary.

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