Help with a walk on an ellipse

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The problem is formally attached in the PDF. I did not see it fit to post my problem on the forum itself (sorry).

Any assistance is appreciated.

Thanks.
 

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hey octohydra, welcome to PF, so you know it usually takes a while for attachments to clear
 
That is fine by me. I felt that this was the best way I could present the problem even if TeX is native to the forum.
 

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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