Vector Definition: Explaining Left Side to Right Side

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Hi For some strange reason I just can't see why this is true?? Can anyone help me explain why the left side can be written as the right side? I added a picture.
 

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The thing that confuses me the most is the p-tu.
 
It's just the associative law for addition of vectors:
(v- p)+ (p- tu)= v+ (-p+ p)- tu= v- tu.
 
Ahh that's the trick huh? So is (v- p)+ (p- tu) a geometric figure? Or just something to be considered as numbers.
 

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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