Hi I am doing a past exam for my complex analysis course and I should just mention right now that while it's a mix of pure/applied math I have never done a pure math unit before and i really really really suck at doing proofs and such..(adsbygoogle = window.adsbygoogle || []).push({});

Given c>0 and f(z) is entire such that |f(z)| ≤ c|z| show that :

f(z)=wz for some complex constant w.

I just have no idea how to tackle problems like this whatsoever and have to turn to google and notes which I obviously wont be able to do in the exam. Also I have trouble remembering all these theorems, corollaries, propositions..

My attempt at a solution was to state Louvilles theorem which is that if:

|f(z)|≤M and f(z) is entire then f(z)=w.. I don't really know where to go from here..

Any tips for tackling problems like this would be really appreciated!

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# Complex analysis - Louvilles Theorem (I think)

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