My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 30th, 2013, 07:31 AM   #21
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 234

Re: Cube roots of -1

I don't want to post anything there because I would prefer to keep that post clean for any wandering transcendental number theorist that may happen to pass by.

For your first bullet (by first bullet, I am referring to the top bullet), you are asking about the kobayashi maru style cheats (which I like all of them BTW) presented by [color=#0000FF]crom[/color], [color=#00FF00]mathbalarka[/color] and [color=#00FF00]Hoempa[/color]? If yes, then I think there should be many (perhaps infinite) ways to represent root 3.

I don't think I understand the second bullet. Is an algebraic number? Too tired to look it up... If not, then



But like I said, I'm not sure about what you are asking, so bear with me.

agentredlum is offline  
 
December 30th, 2013, 09:17 AM   #22
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Cube roots of -1



Also, note that is also transcendental by Lindemann-Weierstrass theorem. But that does not prove whether or not is algebraic or not.



And is transcendental by Gelfond–Schneider, unfortunately, so I cannot prove or disprove whether your expression holds or not.

PS : That should have been but similar consideration holds and we have nothing much.

PPS : You can post this on that topic, as I believe it is non trivial enough to get considerations from those transcendental passer by s... Oops, I mean transcendental number theorist passer-by s...
mathbalarka is offline  
December 30th, 2013, 11:34 PM   #23
Global Moderator
 
Joined: Dec 2006

Posts: 21,128
Thanks: 2337



When using latex, type \ln rather than just ln for the ln function.

Quote:
Originally Posted by mathbalarka
Incorrect.
skipjack is offline  
December 31st, 2013, 12:37 AM   #24
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Cube roots of -1

Quote:
Originally Posted by skipjack
Incorrect.
Right, . I am not sure whether this would effect anything (most probably would), I have to take a look at it seriously later.
mathbalarka is offline  
December 31st, 2013, 03:57 AM   #25
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 234

Re:

Quote:
Originally Posted by skipjack
As usual [color=#BF0000]skipjack[/color] has posted the best answer so far. I did it a little bit differently, first, as a matter of personal preference,



And that's what I used.

Second, if you know one root you can get the others by using symmetry and rotations.

Multiplication by rotates a point counterclockwise in the complex plane by 90°.

Multiplication by rotates a point counterclockwise in the complex plane by 45°.

...etc.

In general, if you want to rotate counterclockwise by N°, multiply by



So, I know one root of is x = -1.

I know the roots are symmetrically located at intervals of 120° = 360°/3.

I can use as a rotation machine.

To rotate x = -1, multiply it like so,



There's another root, now do it again,



And there's the other root.

Anyway, hope you see how to play around with multiplications additions and rotations.

agentredlum is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
cube, roots



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Cube roots of unity question 2 Dean1884 Algebra 4 August 16th, 2013 09:03 PM
Cube roots of unity question 1.. Dean1884 Algebra 3 August 16th, 2013 01:37 AM
Finding Cube Roots using Geometry long_quach Geometry 10 February 19th, 2013 01:11 AM
Derivative of cube roots and trig imcutenfresa Calculus 1 September 20th, 2009 05:34 AM
Three cube roots of 1 dequinox Complex Analysis 1 June 9th, 2009 03:00 PM





Copyright © 2019 My Math Forum. All rights reserved.