Simple dot product [inner product] (verification)

seto6
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Homework Statement


2v1m3ax.png



Homework Equations



know dot product

The Attempt at a Solution


PART A
2cr2ij6.png


PART B
not sure what's it asking for

help would be great
 
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Well, what you posted is the answer to the B part actually :wink: Notice the "for all v" part in A. Specific example of u,v does the trick for B, not for A. Hint for A: (u-w)*v = 0 for all v. What does it say about u - w?
 

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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