Circulation over a triangle in R^3

sriracha
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I have attached a file with all needed information including the function and path of integration. My work seems right to me, but the correct answer is a^2. Will someone please take a look and show me where my misstep is.
 

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Just to be sure, can someone confirm the file opens/ is legible?
 
Yes it opens.
 
thanks
 

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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