How Do Complex Plane Transformations Affect Equations?

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Above is the problem and given solution. I am unable to understand the solution for part b - if x =4 then surely u/(u^2 + v^2) =4. Can someone please clarify this.

Thanks in advance.
 
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Typo is the only thing that comes to mind.

I think it should be 4.
 
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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