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April 19th, 2018, 06:50 PM  #1 
Newbie Joined: Oct 2017 From: sweden Posts: 24 Thanks: 0  Complex root problem
This seems pretty easy, but I cannot seem to have a possible solution for it and it goes: **PROBLEM**: If $a>e$, show that the equation $e^z = az^n$ has $n$ solutions inside the unit circle. Can someone show me how to do these roots problems formally so I can follow up and continue other problems? I would appreciate the help. ( Im studying for my finals atm so I dont have much time to spend each time thinking about problems I am stuck at so I ask for help here). 
April 19th, 2018, 07:27 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 609 Thanks: 378 Math Focus: Dynamical systems, analytic function theory, numerics 
This is a straight forward application of Rouche's theorem.


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