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# FP2 - Roots watch

1. (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.
2. (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.

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!
3. The roots are as shown here.

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
4. (Original post by BabyMaths)
The roots are as shown here.

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)"

5. (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)"

We are given .

So .

The other roots come from

etc.
6. 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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