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April 19th, 2018, 06:50 PM   #1
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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).
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April 19th, 2018, 07:27 PM   #2
SDK
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Math Focus: Dynamical systems, analytic function theory, numerics
This is a straight forward application of Rouche's theorem.
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