Rec, Spherical and cylind coordinates.

catch22
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Homework Statement


upload_2015-12-3_22-19-38.png


Homework Equations

The Attempt at a Solution

here is the setup for each, can someone check if they are correct before I evaluate the volume?
 

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If you get different answers when evaluated, then you will know you made a mistake.
 

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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