Maximizing Contour Integrals: Tips and Tricks

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Hello.
Question is attached.
Can someone check my answer? Did I convert the last part correctly? Is everything correct?
 

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looks OK to me... and what is ##\sin\pi##?
 
Joffan said:
looks OK to me... and what is ##\sin\pi##?

Sin∏=0. Thanks!
 
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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