Path integral/Stokes's and Green's theorem

PhysicsGente
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I meant Line integral.

Homework Statement



I want to find the path integral of a vector function F over a closed path in Euclidean space with z = 0.

Homework Equations


The Attempt at a Solution



I was wondering if it is allowed to first use Stoke's theorem and then Green's theorem. I would end up getting div(curl(F)) which I believe equals to zero. But I am not sure if I'm allowed to use Green's theorem in this case.
 
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Can you post the original problem and your work so far?
 
I have figured it out. Thank you!
 

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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