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    (Original post by kingm)
    i'm with you there, but the answer they have is:

    z = 1 + e^(ipi(1+2k) / 5)
    Yep. I slipped up there. I was cooking dinner too.

    Your first w has argument pi/5. You need 4 more, equally spaced so add on multiples of 2pi/5.
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    (Original post by BabyMaths)
    Yep. I slipped up there. I was cooking dinner too.

    Your first w has argument pi/5. You need 4 more, equally spaced so add on multiples of 2pi/5.
    You're really helpful but i am clearly missing something entirely fundamental about this.

    To get from (z-1)^5=-1

    to the answer, z=1+e^(ipi(1+2k)/5), with what you've advised i.e w=z-1, is simply not happening for me. Stress town over here!
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    The roots are as shown here.

    Name:  fifth roots  of -1.png
Views: 28
Size:  14.4 KB

    You see that they are equally spaced and have arguments

    pi/5

    pi/5 + 2pi/5

    pi/5 + 2 x 2pi/5

    pi/5 + 3 x 2pi/5

    pi/5 + 4 x 2pi/5

    I copied the diagram for roots of unity from wikipedia and reflected to get roots of -1
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    (Original post by BabyMaths)
    The roots are as shown here.

    Name:  fifth roots  of -1.png
Views: 28
Size:  14.4 KB

    You see that they are equally spaced and have arguments

    pi/5

    pi/5 + 2pi/5

    pi/5 + 2 x 2pi/5

    pi/5 + 3 x 2pi/5

    pi/5 + 4 x 2pi/5

    I copied the diagram for roots of unity from wikipedia and reflected to get roots of -1
    Its the maths side of getting to their answer that i don't understand.

    I get "z = 1 - e^(2kipi / 5)"

    They get "z = 1 + e^(ipi(1+2k)/5)"

    2 completely different answers.
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    (Original post by kingm)
    Its the maths side of getting to their answer that i don't understand.

    I get "z = 1 - e^(2kipi / 5)"

    They get "z = 1 + e^(ipi(1+2k)/5)"

    2 completely different answers.
    We are given z_1=1+e^{\pi i/5}.

    So z_1-1= e^{\pi i/5}.

    The other roots come from

    z_1-1= e^{\pi i/5}

    z_2-1= e^{\pi i/5 + 2\pi i /5}

    z_3-1= e^{\pi i/5 + 2\times 2\pi i /5}

    etc.
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    Ok dude, really appreciate your help. Seeing a tutor next week to clarify some things anyway. Maths is pretty hard teach online i think :-). Hope your dinner wasn't burnt!
 
 
 
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Updated: December 30, 2012
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