Prove if a vector field is conservative or not

jessedevin
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How do you prove if a vector field is conservative or if it isn't conservative?
For example, if we have the vector field F(x, y, z) = x^2yz ı + y  + x^2 k, how do we find out if it is conservative or not conservative?
 
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Find the curl of that vector field, and figure out the significance if it is zero.

Zz.
 

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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