anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
axes not aces
anonymous
  • anonymous
@nincompoop @Michele_Laino @Nnesha @Luigi0210 @whpalmer4 @uri @jhonyy9 @sleepyjess
anonymous
  • anonymous
Man I know how to do this, but not sure how to explain it /:

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

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