nth roots of unity ??? - Math Help Forum

$Math Help Forum$

$Go Back$		Math Help Forum > Pre-University Math Help > Pre-Algebra and Algebra
$Reload this Page$ nth roots of unity ???

Download MHF Flyer

Mark Forums Read

$Reply$

#1

$Old$ January 7th, 2009, 07:46 PM

dixie $dixie is offline$

Newbie

Join Date: Aug 2008

Posts: 15

Country:

United States

Thanks: 14

Thanked 0 Times in 0 Posts

$dixie is on a distinguished road$

$Default$ nth roots of unity ???

for which n is i an nth root of unity?

hmm, thanks

$Reply With Quote$

Advertisement

#2

$Old$ January 7th, 2009, 09:44 PM

Math Major $Math Major is offline$

Junior Member

Join Date: Jan 2009

Location: Tallahassee

Posts: 34

Country:

United States

Thanks: 2

Thanked 12 Times in 12 Posts

$Math Major is on a distinguished road$

$Default$

A root of unity is a complex number that yields 1 when raised to some nth root.

i is defined to be (-1)^(1/2)
i^2 then would be (-1)^(1/2)^2 = (-1)^(2/2) = (-1)^1 = -1
i^3 would be i^2 * i = -1 *i = -1
i^4 would be i^2 * i^2 = -1 * -1 = 1

Every fourth term will result in a value of 1.

$Reply With Quote$

The following users thank Math Major for this useful post:
dixie
$Donate to MHF$

#3

$Old$ January 7th, 2009, 09:44 PM

$mr fantastic's Avatar$

mr fantastic $mr fantastic is offline$

Flow Master

Join Date: Dec 2007

Location: Zeitgeist

Posts: 12,226

Country:

Australia

Thanks: 2,574

Thanked 4,756 Times in 4,189 Posts

$mr fantastic has a reputation beyond repute$ $mr fantastic has a reputation beyond repute$ $mr fantastic has a reputation beyond repute$ $mr fantastic has a reputation beyond repute$ $mr fantastic has a reputation beyond repute$ $mr fantastic has a reputation beyond repute$ $mr fantastic has a reputation beyond repute$ $mr fantastic has a reputation beyond repute$ $mr fantastic has a reputation beyond repute$ $mr fantastic has a reputation beyond repute$ $mr fantastic has a reputation beyond repute$

$Default$

Quote:

Originally Posted by dixie $View Post$

for which n is i an nth root of unity?

hmm, thanks

The nth roots of unity are $\cos \left( \frac{2 \pi}{n}\right) + i \, \sin \left( \frac{2 \pi}{n}\right)$ .

So you require the integer values of n such that $\sin \left( \frac{2 \pi}{n}\right) = 1 \, ....$

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.

$Reply With Quote$

The following users thank mr fantastic for this useful post:
dixie
$Donate to MHF$

$Reply$

« prove i^2 =-1 | Top | Algebraic Development of the Quadratic Formula »

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Posting Rules
You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are Off

Forum Jump

All times are GMT -7. The time now is 06:26 PM.

your link here Sponsors

rv solar, e-learning,

Math Help Forum is a community of maths forums with an emphasis on maths help in all levels of mathematics.
Register to post your math questions or just hang out and try some of our math games or visit the arcade.