I'm not sure I understand how to do this. Thanks for the help! Find all seventh roots of unity and sketch them on the aces below. http://www.google.com/imgres?imgurl=http%3A%2F%2Fuser-content.enotes.com%2F7c4540d5f581a45d753fc2cff4180d9b3cb69630_thumb.png&imgrefurl=http%3A%2F%2Fwww.enotes.com%2Fhomework-help%2Ffind-all-seventh-roots-unity-sketch-them-axes-436533&h=287&w=282&tbnid=aGzfxmKJbQW5JM%3A&zoom=1&docid=WUxe1gxLnyuV-M&ei=pg55U7atMtOSqAbAgYGIAQ&tbm=isch&client=safari&ved=0CFUQMygBMAE&iact=rc&uact=3&dur=849&page=1&start=0&ndsp=32

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I'm not sure I understand how to do this. Thanks for the help! Find all seventh roots of unity and sketch them on the aces below. http://www.google.com/imgres?imgurl=http%3A%2F%2Fuser-content.enotes.com%2F7c4540d5f581a45d753fc2cff4180d9b3cb69630_thumb.png&imgrefurl=http%3A%2F%2Fwww.enotes.com%2Fhomework-help%2Ffind-all-seventh-roots-unity-sketch-them-axes-436533&h=287&w=282&tbnid=aGzfxmKJbQW5JM%3A&zoom=1&docid=WUxe1gxLnyuV-M&ei=pg55U7atMtOSqAbAgYGIAQ&tbm=isch&client=safari&ved=0CFUQMygBMAE&iact=rc&uact=3&dur=849&page=1&start=0&ndsp=32

Mathematics
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axes not aces
Man I know how to do this, but not sure how to explain it /:

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We want to solve the equation \( \large z^7 = 1 \) $$\large{ 1= \cos(2\pi k) + i \sin(2\pi k ), k \in \mathbb Z \\\text {by substitution} \\z^7= \cos(0+2\pi k) + i \sin(0+2\pi k ) \\\text {by demoivres theorem} \\z^7= \cos(2\pi k/7) + i \sin(2\pi k/7 ), k = 0,1,2,3,4,5,6 }$$
Once I have all that, it should look like this: https://www.wolframalpha.com/input/?i=x^7-1%3D0 ?
For the bottom graph
If you click on approximate form you can get the decimal values.
Is it okay if I have help with the graphing?
yes
there is a picture here http://prntscr.com/7h01sn
But it doesn't have the radian values. Is there a way to graph it with the radians there?
You mean on your graph? There isn't shown pi/7.
The best you can do is estimate where to plot it
Okay
the first point is (1,0) that is clear
then the next point is (cos 2pi/7, sin(2pi/7)) where is the angle 2pi/7 relative to pi/6 and pi/6
all the points will be on the unit circle
|dw:1434318947436:dw| Would I draw it at the first mini circle in this graph?
|dw:1434319023208:dw|
The dot is (1,0)?
http://prntscr.com/7h04hm
okay, thanks
The rest are drawn around the 1 area?
thats correct. It might be easier to conver the radian angles to degrees 2pi/7 * 180/pi = 51.43 degrees approximately
Should I draw a line connecting the dot?
pi/4 is 45 degrees pi/3 is 60 degrees So the second point will be between these two angles.
52.5 ok
I believe we should just plot the points. But if you do connect the points you will get a 7 sided regular polygon, a heptagon.
I meant to the center, like wolfram. Do you think that would be fine, or should I leave it be?
http://prntscr.com/7h06t4
I don't see wolfram plotting to the center, can you show me?
There is a line connecting the dots to the center. It's grey.
I see it now. Those are optional.
The main thing are the points.
okay, cool
Can you help me with the rest of the points?
convert the radian angles to degrees, that might be easier
Cool. Thanks for the help! I gave you a medal :)
Your welcome :)

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