Applying Green's Theorem: Solving Parametrized Homework Problems

nysnacc
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Homework Statement


upload_2016-11-9_16-32-46.png


Homework Equations


Green's theorem

The Attempt at a Solution


DO I first parametrize? For 1st part, I have 3 parametrizations, which I can then find the normal vector, and use in the integrals?
 
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I'm sure there are examples of similar problems worked out in your textbook. Try using them as a model for solving these problems.
 

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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