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

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

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

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4But how will I show that they are the only ones?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4@Opcode and @experimentX any ideas?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4Well... \(a^2 + b^2 = 1\)

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1I think you don't mean http://en.wikipedia.org/wiki/Gaussian_units you mean http://en.wikipedia.org/wiki/Gaussian_integer

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4I mean Gaussian units. See my first post

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

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

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4OK yeah, I mean that they are a unit.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1units of Gaussian Integer ... looks like related to ring theory.

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

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4Ring theory is a subset of abstract algebra. This is theoretical mathematics also known as pure mathematics.

Opcode
 2 years ago
Best ResponseYou've already chosen the best response.0What would you even need this for? Like job wise?

ParthKohli
 2 years ago
Best 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

experimentX
 2 years ago
Best 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.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4@experimentX Can we call this complex analysis?

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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1I 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.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1I think abstract algebra is at more fundamental level than complex analysis.

Opcode
 2 years ago
Best ResponseYou've already chosen the best response.0How old are you experimentX? (If I may ask?)

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1celebrating 25th spring

Opcode
 2 years ago
Best ResponseYou've already chosen the best response.0Wow. You guys are so smart! I feel so dumb around you guy :(

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

Opcode
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, very smart indeed. @ParthKohli you education is so beautiful :)

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

SWAG
 2 years ago
Best ResponseYou've already chosen the best response.1http://blog.openstudy.com/wpcontent/uploads/2012/06/ParthSmartScoreProfilecopy.png

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4That's a pretty old screenshot. :)

SWAG
 2 years ago
Best ResponseYou've already chosen the best response.1Lol yeah i found it on google images

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4yeah, they had written a blog post on me. _

SWAG
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah I see its about how young you are haha

Opcode
 2 years ago
Best 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 :)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4@SWAG It's about how young and stupid I am. :)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4@Opcode No! There are people much better than me: @DLS and @shubhamsrg

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1looks 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.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4Wow, you could do trig?! WOW!

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1simple trigonometry ... that's the best i could do.

Opcode
 2 years ago
Best ResponseYou've already chosen the best response.0Pssh, 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

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

Opcode
 2 years ago
Best ResponseYou've already chosen the best response.0Yush ^_^. I need to start using Facebook more anyway :) Onward!

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

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

Opcode
 2 years ago
Best ResponseYou've already chosen the best response.0Boop ^.^ http://cdn.memegenerator.net/instances/400x/35373413.jpg

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.4Don't. Start. Parth. Kohli. Memes. I'm. Not. Chuck. Norris.

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0Well I don;t dare to offend The Parth Kohli.

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

Opcode
 2 years ago
Best ResponseYou've already chosen the best response.0Would you like a shubhamsrg meme :3

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0I 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.

Opcode
 2 years ago
Best ResponseYou've already chosen the best response.0Next time if anyone calls you dumb use the ParthKohli defense!

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0ofcorse , as I said, I am gonna show him this screenshot! :)

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0Because when he says it, it can't be wrong!

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

Opcode
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm. Can I possible get a Ph. D in history? Or is that a no?

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