Complex Analysis: Entire function dominated by another entire function

michael.wes
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Homework Statement



If f,g are entire functions and |f(z)| <= |g(z)| for all z, draw some conclusions about the relationship between f and g

Homework Equations



none

The Attempt at a Solution



I just need a push in the right direction.. thanks for any and all help!
 
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Do you know Louiville's Theorem?
 
Gib Z said:
Do you know Louiville's Theorem?

Thanks, I got it now :)
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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