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Homework Help: Find the real part

  1. Oct 7, 2012 #1


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    1. The problem statement, all variables and given/known data
    If [itex]\large α = e^{i\frac{8∏}{11}}[/itex], then find [itex]Re(α+α^{2}+α^{3}+α^{4}+α^{5})[/itex]

    2. Relevant equations

    3. The attempt at a solution
    [itex]\large e^{i\frac{8∏}{11}}+e^{i\frac{16∏}{11}}............+e^{i\frac{40∏}{11}}[/itex]

    [itex]cos \frac{8∏}{11}+isin \frac{8∏}{11}..........[/itex]

    Since I am interested only in real part so now I have to find the value of


    where [itex]θ= \frac{8∏}{11}[/itex]

    I think some trigonometry must be applied since it seems to me sum of a trigonometrical series.
  2. jcsd
  3. Oct 7, 2012 #2


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    Is not


    a geometric series?

  4. Oct 7, 2012 #3

    Ray Vickson

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    You have found the real part; it is a sum of 5 terms. What is wrong with that answer?

  5. Oct 8, 2012 #4


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    Hey I have found the answer but not completely. I have to find the value of cosθ+cos2θ.....
    which I dont know how to solve
  6. Oct 8, 2012 #5


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    Well as people have already mentioned, the answer IS
    but that's messy, and this question has been cleverly constructed so that there is a nice answer.



    Now, notice that

    [tex]\alpha^6=e^{48\pi i/11}=e^{4\pi i/11}=\left(e^{8\pi i/11}\right)^{1/2}=\alpha^{1/2}[/tex]

    So we can now turn the expression into



    I'm sure you can finish it off from here :smile:
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