Question

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%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

Answer 1

since \(1^7=1\) you know one answer, namely 1
`

Answer 2

divide the circle up in to seven equal parts, with 1 as one of them

Answer 3

Is there a formula to follow?

Answer 4

@satellite73

Answer 5

no, that is all

Answer 6

if you want the nth roots of 1, divide the circle in to n parts
finish

Answer 7

not sure I understand :(

Answer 8

it is the same thing we did before

Answer 9

but of 1?

Answer 10

one answer is 1 right?

Answer 11

if you want to be real silly you can write
\[1=\cos(0)+i\sin(0)\]

Answer 12

divide the angle by 7 and you still get
\[\cos(0)+i\sin(0)\]

Answer 13

then add \(2\pi\) , divide by 7 and get
\[\cos(\frac{2\pi}{7})+i\sin(\frac{2\pi}{7})\]

Answer 14

wouldn't it be like this? https://www.wolframalpha.com/input/?i=x^7-1%3D0

Answer 15

all you are doing is dividing the circle up in to seven equal parts

Answer 16

okay, so if I do the same as before I'll end up with different results to graph?

Answer 17

yeah look at the wolf picture
they have the unit circle divided in to seven equal pieces

Answer 18

So dividing by 7 and adding 2pi does the same?

Answer 19

You'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

Answer 20

I thought theta was 0

Answer 21

For 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

Answer 22

According to satellites thing

Answer 23

satellite's

Answer 24

that happens when k = 0

there are 6 other roots of unity though

Answer 25

gotcha

Answer 26

So I make it equal 1, 2, .. and solve?

Answer 27

something like this