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anonymous
 one year ago
Thanks for helping!
I'm not sure I understand this problem:
II need to find all seventh roots of unity and sketch them on this axes.
http://www.google.com/imgres?imgurl=http%3A%2F%2Fusercontent.enotes.com%2F7c4540d5f581a45d753fc2cff4180d9b3cb69630_thumb.png&imgrefurl=http%3A%2F%2Fwww.enotes.com%2Fhomeworkhelp%2Ffindallseventhrootsunitysketchthemaxes436533&h=287&w=282&tbnid=aGzfxmKJbQW5JM%3A&zoom=1&docid=WUxe1gxLnyuVM&ei=pg55U7atMtOSqAbAgYGIAQ&tbm=isch&client=safari&ved=0CFUQMygBMAE&iact=rc&uact=3&dur=849&page=1&start=0&ndsp=32
anonymous
 one year ago
Thanks for helping! I'm not sure I understand this problem: II need to find all seventh roots of unity and sketch them on this axes. http://www.google.com/imgres?imgurl=http%3A%2F%2Fusercontent.enotes.com%2F7c4540d5f581a45d753fc2cff4180d9b3cb69630_thumb.png&imgrefurl=http%3A%2F%2Fwww.enotes.com%2Fhomeworkhelp%2Ffindallseventhrootsunitysketchthemaxes436533&h=287&w=282&tbnid=aGzfxmKJbQW5JM%3A&zoom=1&docid=WUxe1gxLnyuVM&ei=pg55U7atMtOSqAbAgYGIAQ&tbm=isch&client=safari&ved=0CFUQMygBMAE&iact=rc&uact=3&dur=849&page=1&start=0&ndsp=32

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0since \(1^7=1\) you know one answer, namely 1 `

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0divide the circle up in to seven equal parts, with 1 as one of them

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is there a formula to follow?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if you want the nth roots of 1, divide the circle in to n parts finish

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure I understand :(

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is the same thing we did before

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0one answer is 1 right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if you want to be real silly you can write \[1=\cos(0)+i\sin(0)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0divide the angle by 7 and you still get \[\cos(0)+i\sin(0)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then add \(2\pi\) , divide by 7 and get \[\cos(\frac{2\pi}{7})+i\sin(\frac{2\pi}{7})\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wouldn't it be like this? https://www.wolframalpha.com/input/?i=x^71%3D0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0all you are doing is dividing the circle up in to seven equal parts

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so if I do the same as before I'll end up with different results to graph?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah look at the wolf picture they have the unit circle divided in to seven equal pieces

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So dividing by 7 and adding 2pi does the same?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1You'll have 7 roots of unity of the form \[\Large \cos(\frac{2\pi}{7}*k)+i\sin(\frac{2\pi}{7}*k)\] where k is an integer and k runs from k = 0 to k = 6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought theta was 0

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1For n roots of unity, you'll have n roots of the form \[\Large \cos(\frac{2\pi}{n}*k)+i\sin(\frac{2\pi}{n}*k)\] k will be an integer from k = 0 to k = n

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0According to satellites thing

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1that happens when k = 0 there are 6 other roots of unity though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I make it equal 1, 2, .. and solve?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1something like this dw:1434596805847:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1plug in k = 0 through k = 6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but is there a way to measure the coordinates specifically?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah using \[\Large \cos(\frac{2\pi}{7}*k)+i\sin(\frac{2\pi}{7}*k)\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1plug in k = 0 through k = 6

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if k = 0, the whole thing is 1+0i

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434597029810:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1next plug in k = 1 \[\Large \cos(\frac{2\pi}{7}*k)+i\sin(\frac{2\pi}{7}*k)\] \[\Large \cos(\frac{2\pi}{7}*1)+i\sin(\frac{2\pi}{7}*1)\] \[\Large \cos(\frac{2\pi}{7})+i\sin(\frac{2\pi}{7})\] that approximates to 0.6234898+0.78183148i

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434597231701:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is there a way to graph that accurately on the graph above?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if you want, you can raise 0.6234898+0.78183148i to the 7th power you should get 1 as a result

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1with software, yes

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you can use geogebra as that's what I would use

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Geogebra doesn't seem to have a function for this

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1it supports trig functions like sin, cos, etc

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1this is what I get with geogebra

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, I'll use this then. So for work, I can just show cis(2pi/7*k)? for k=06?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for the help!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1cis(2pi/7*k) doesn't work so type in cos(2pi/7*k)+i*sin(2pi/7*k) and replace k with 0 through 6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For work in my worksheet I meant, sorry. Thanks for the help!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would it work for work?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah your teacher should accept cis as shorthand for cos + i*sin

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0awesome :D Thanks for the help!
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