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What is the difference between the Argument Principal and the Rouche's Theorem.

I am not sure when to use which one when I have a question for example:

How many roots of $z^4 + z^3 + 1=0$ lie inside $C=\{|z|=3/2\}$

http://mathworld.wolfram.com/ArgumentPrinciple.html

http://mathworld.wolfram.com/RouchesTheorem.html

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