Analytic Function Homework: Exp[(z^3+1)/(z-1)]

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Homework Statement



Determine the largest subset of C (complex numbers) on which the following function is analytic.

Homework Equations



exp[(z^3+1)/(z-1)]

The Attempt at a Solution



I don't really understand what analytic means, and am having trouble starting this question.
 
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Then you had better look up "analytic" in your textbook!
 
i know what it means, as in the definition etc

im just not sure how to go about finding the largest subset.
 
could someone please give me some help on this question, as i really don't understand it.
 
Where is the derivative of the function defined? Where is it undefined?
 

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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