Vector Field Homework: Learn What's Involved

athrun200
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Homework Statement



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Homework Equations





The Attempt at a Solution


What's surprise?
And is my work correct?


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You have a problem: \mathbf{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}.
 
hunt_mat said:
You have a problem: \mathbf{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}.

r is the radius from centre, isn't it?
 
It is.
 
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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