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

- anonymous

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- anonymous

axes not aces

- anonymous

@nincompoop @Michele_Laino @Nnesha @Luigi0210 @whpalmer4 @uri @jhonyy9 @sleepyjess

- anonymous

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

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## More answers

- 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

Once I have all that, it should look like this: https://www.wolframalpha.com/input/?i=x^7-1%3D0 ?

- anonymous

For the bottom graph

- anonymous

If you click on approximate form you can get the decimal values.

- anonymous

Is it okay if I have help with the graphing?

- anonymous

yes

- anonymous

there is a picture here
http://prntscr.com/7h01sn

- anonymous

But it doesn't have the radian values. Is there a way to graph it with the radians there?

- anonymous

You mean on your graph? There isn't shown pi/7.

- anonymous

The best you can do is estimate where to plot it

- anonymous

Okay

- anonymous

the first point is (1,0) that is clear

- 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

all the points will be on the unit circle

- anonymous

|dw:1434318947436:dw| Would I draw it at the first mini circle in this graph?

- anonymous

|dw:1434319023208:dw|

- anonymous

The dot is (1,0)?

- anonymous

http://prntscr.com/7h04hm

- anonymous

okay, thanks

- anonymous

The rest are drawn around the 1 area?

- anonymous

thats correct.
It might be easier to conver the radian angles to degrees
2pi/7 * 180/pi = 51.43 degrees approximately

- anonymous

Should I draw a line connecting the dot?

- anonymous

pi/4 is 45 degrees
pi/3 is 60 degrees
So the second point will be between these two angles.

- anonymous

52.5 ok

- 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

I meant to the center, like wolfram. Do you think that would be fine, or should I leave it be?

- anonymous

http://prntscr.com/7h06t4

- anonymous

I don't see wolfram plotting to the center, can you show me?

- anonymous

There is a line connecting the dots to the center. It's grey.

- anonymous

I see it now. Those are optional.

- anonymous

The main thing are the points.

- anonymous

okay, cool

- anonymous

Can you help me with the rest of the points?

- anonymous

convert the radian angles to degrees, that might be easier

- anonymous

Cool. Thanks for the help! I gave you a medal :)

- anonymous

Your welcome :)

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