Vectors and Coordinate Systems

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Hi, I'm a first year university student and I don't understand vectors and the coordinate system. I tried reading the book, but it doesn't make sense to me like the magnitude of theta and sigma or the oval with the vertical line through it. If someone could help me with the concept of it and the components, that would be great, thanks. :smile:
 
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This tutorial might help: http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html
Or this one: http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html#veccon

But you'll get more specific help by attempting to do some problems from your book. Post the problems that stump you, along with your attempted solutions, and then you'll get the exact help you need.
 
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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