How Do You Compute the Flux of a Vector Field Through a Circle?

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Homework Statement


Let C be the circle of radius 2 centered on the origin and contained in the plane 2x - 3y + 5 = 0. Compute the flux through C of the constant vector field v = {6, - 1, 12}

I have no idea about this problem. This is one the review problem which was given to us in the class for next week's exam.
 
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Well, what is the definition (it involves an area integral) of flux of a vector field through a surface?

What is the surface in this case? What is the unit normal to that surface?
 

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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