Converting fifth roots from polar form to complex

Braka
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Homework Statement


I am looking for the fifth roots of unity, which I believe come in the form of:

cos(2kpi/5) + isin(2kpi/5), k=1,2,3,4,5 and when k=5, the complex number is 1.

how do you convert the rest to complex numbers? Normally, I use common triangles like:

45-45-90 and 30-60-90

but I don't think there is a triangle for 2pi/5.


Homework Equations





The Attempt at a Solution

 
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I don't understand your question. cos(2kpi/5) + isin(2kpi/5) is a complex number. Do you want to convert that into polar form? It should be pretty obvious.
 
Its obvious? I can't recall how to get it. What I meant is I wanted to put it in a +bi form. That is my problem. Sorry for stating it in a confusing manner
 
It is already in the form a+bi.
a=cos(2kpi/5)
b=sin(2kpi/5)
 
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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