Converting fifth roots from polar form to complex

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Homework Help Overview

The discussion revolves around finding the fifth roots of unity expressed in polar form and converting them into the standard complex number format a + bi. The original poster expresses uncertainty about how to achieve this conversion, particularly for angles like 2π/5.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to convert the polar form of the fifth roots of unity into a + bi format, questioning how to do so without a known triangle for the angle involved. Other participants clarify that the expression is already in the desired form and discuss the components a and b.

Discussion Status

The conversation is ongoing, with some participants providing clarification about the representation of the complex numbers. There is a mix of understanding and confusion regarding the conversion process, indicating that further exploration of the topic may be needed.

Contextual Notes

The original poster's confusion seems to stem from a lack of familiarity with the specific angle involved in the conversion, as well as the use of common triangles for reference. The discussion does not resolve this uncertainty but highlights differing levels of understanding among participants.

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)
 

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