Cauchy Random Variable Homework with Equations and Attempt

ahamdiheme
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Homework Statement


I have attached the problem statement


Homework Equations



Also find attached

The Attempt at a Solution



My attempt is attached together with the problem statement and the relevant equations.
 

Attachments

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Is anyone going to help me out on this one? I need your help. Here i will re-post as .jpg. Thank you
 

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    Problem.jpg
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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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