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Show that \(1\), \(1\), \(i\) and \(i\) are the only Gaussian units and that there are no other Gaussian units.
 one year ago
 one year ago
Show that \(1\), \(1\), \(i\) and \(i\) are the only Gaussian units and that there are no other Gaussian units.
 one year ago
 one year ago

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ParthKohliBest ResponseYou've already chosen the best response.4
A Gaussian unit is a Gaussian integer \(z\) such that \(\dfrac{1}{z}\) is also a Gaussian integer.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
Well, we essentially want to show that \(\pm i,\pm 1\; \; 1\) and they are the only ones.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
But how will I show that they are the only ones?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
@Opcode and @experimentX any ideas?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
No .. have to see.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
Well... \(a^2 + b^2 = 1\)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
I think you don't mean http://en.wikipedia.org/wiki/Gaussian_units you mean http://en.wikipedia.org/wiki/Gaussian_integer
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
I mean Gaussian units. See my first post
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Sorry! Opcode is still learning trigonometry. No "Gaussian units" for now :( Mabye @Hero ?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
looks like there is solution on M.SE http://math.stackexchange.com/questions/108071/uniqueunitsofgaussianintegers
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
OK yeah, I mean that they are a unit.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
units of Gaussian Integer ... looks like related to ring theory.
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
What math is this? I see on the MSE thing it says: abstractalgebra, ringtheory. So is it both?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
Ring theory is a subset of abstract algebra. This is theoretical mathematics also known as pure mathematics.
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
What would you even need this for? Like job wise?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
@Opcode that is why they say that among a Ph.D in physics, a Ph.D in CS, a Ph.D in theoretical math and a large pepperoni pizza, the most different thing is a Ph.D in theoretical math. The other three can feed a family of four XD
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
@Opcode the abstract algebra is the generalization of the algebra we do. They make use of properties of these algebraic structures to solve the problem than we solve things directly.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
@experimentX Can we call this complex analysis?
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Ouch. So much things to learn _ If I was to attempt to get a Ph. D I'd be at age 40 :(.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
I think you can't .... I haven't so far explored the depths of complex analysis. But I know these types of things get's mumbledjumbled up.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
I think abstract algebra is at more fundamental level than complex analysis.
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
How old are you experimentX? (If I may ask?)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
celebrating 25th spring
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Wow. You guys are so smart! I feel so dumb around you guy :(
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Just below average old guy!! There is nothing wow about me ... Looks like parth will grow up to be smart guy.
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Yes, very smart indeed. @ParthKohli you education is so beautiful :)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
Aw, no! I will grow up to be some oldstreet beggar. You, my friend, have a huge market value. YOU SMARTYPANTS PROGRAMMER!
 one year ago

SWAGBest ResponseYou've already chosen the best response.1
http://blog.openstudy.com/wpcontent/uploads/2012/06/ParthSmartScoreProfilecopy.png
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
That's a pretty old screenshot. :)
 one year ago

SWAGBest ResponseYou've already chosen the best response.1
Lol yeah i found it on google images
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
yeah, they had written a blog post on me. _
 one year ago

SWAGBest ResponseYou've already chosen the best response.1
Yeah I see its about how young you are haha
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
@ParthKohli I'd rather be dumb in programming and have your math skills. Heck I'd even drop studying history. @ParthKohli is my role model :)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
@SWAG It's about how young and stupid I am. :)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
@Opcode No! There are people much better than me: @DLS and @shubhamsrg
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
looks like @ParthKohli is being modest ,,, don't you go to school? When i was thirteen i was in eighth grade. I could do simple trigonometry.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
Wow, you could do trig?! WOW!
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
simple trigonometry ... that's the best i could do.
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Pssh, tell the truth: Look at Parth: http://blog.openstudy.com/2012/06/27/ouryoungestuserandquickestto99/ I can do simple trigonometry... :3 Parth taught me the basics :P I found the rest by internet :D
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
Juzt sho berry Amaysing! :O I am going to create a parth kohli fan club on facebook now.
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Yush ^_^. I need to start using Facebook more anyway :) Onward!
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Just a joke Parth :) I'm wasting away in class : I really should be listening >.>
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
http://www.facebook.com/groups/499948566734706/
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Not joining that group... When Parth says "..." It means > No. Just No. *Any then the Parth meme was born :O*
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Boop ^.^ http://cdn.memegenerator.net/instances/400x/35373413.jpg
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.4
Don't. Start. Parth. Kohli. Memes. I'm. Not. Chuck. Norris.
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
Well I don;t dare to offend The Parth Kohli.
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Opcode promises this is the last one: http://cdn.memegenerator.net/instances/400x/35373583.jpg Now back to studying _
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
http://gyazo.com/73d47564ed85f1b06dcf4d05f3a8eae6
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Would you like a shubhamsrg meme :3
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
I am gonna set that image as my desktop wallpaper, my room wallpaper, even gonna get it tatooed . Gonna preserve its print out like a certificate.. The Parth Kohli said that! wow! that is gonna help me in my future.
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Next time if anyone calls you dumb use the ParthKohli defense!
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
ofcorse , as I said, I am gonna show him this screenshot! :)
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
Because when he says it, it can't be wrong!
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
Not that I am agreeing what he is saying, but he has said it, so no one can argue.
 one year ago

OpcodeBest ResponseYou've already chosen the best response.0
Hmm. Can I possible get a Ph. D in history? Or is that a no?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
Only one person can answer all the questions in the world! Yes thats right,! We all know who that is. ^_^
 one year ago
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