ParthKohli
  • ParthKohli
Show that \(1\), \(-1\), \(i\) and \(-i\) are the only Gaussian units and that there are no other Gaussian units.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ParthKohli
  • ParthKohli
A Gaussian unit is a Gaussian integer \(z\) such that \(\dfrac{1}{z}\) is also a Gaussian integer.
ParthKohli
  • ParthKohli
Well, we essentially want to show that \(\pm i,\pm 1\; |\; 1\) and they are the only ones.
ParthKohli
  • ParthKohli
But how will I show that they are the only ones?

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ParthKohli
  • ParthKohli
@Opcode and @experimentX any ideas?
experimentX
  • experimentX
No .. have to see.
ParthKohli
  • ParthKohli
Well... \(a^2 + b^2 = 1\)
experimentX
  • experimentX
I think you don't mean http://en.wikipedia.org/wiki/Gaussian_units you mean http://en.wikipedia.org/wiki/Gaussian_integer
ParthKohli
  • ParthKohli
I mean Gaussian units. See my first post
Opcode
  • Opcode
Sorry! Opcode is still learning trigonometry. No "Gaussian units" for now :( Mabye @Hero ?
experimentX
  • experimentX
looks like there is solution on M.SE http://math.stackexchange.com/questions/108071/unique-units-of-gaussian-integers
ParthKohli
  • ParthKohli
OK yeah, I mean that they are a unit.
experimentX
  • experimentX
units of Gaussian Integer ... looks like related to ring theory.
ParthKohli
  • ParthKohli
ah! nice
Opcode
  • Opcode
What math is this? I see on the MSE thing it says: abstract-algebra, ring-theory. So is it both?
ParthKohli
  • ParthKohli
Ring theory is a subset of abstract algebra. This is theoretical mathematics also known as pure mathematics.
Opcode
  • Opcode
What would you even need this for? Like job wise?
ParthKohli
  • ParthKohli
@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 X-D
experimentX
  • experimentX
@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
  • ParthKohli
@experimentX Can we call this complex analysis?
Opcode
  • Opcode
Ouch. So much things to learn -_- If I was to attempt to get a Ph. D I'd be at age 40 :(.
experimentX
  • experimentX
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 mumbled-jumbled up.
experimentX
  • experimentX
I think abstract algebra is at more fundamental level than complex analysis.
Opcode
  • Opcode
How old are you experimentX? (If I may ask?)
experimentX
  • experimentX
celebrating 25th spring
Opcode
  • Opcode
Wow. You guys are so smart! I feel so dumb around you guy :(
experimentX
  • experimentX
Just below average old guy!! There is nothing wow about me ... Looks like parth will grow up to be smart guy.
Opcode
  • Opcode
Yes, very smart indeed. @ParthKohli you education is so beautiful :-)
ParthKohli
  • ParthKohli
Aw, no! I will grow up to be some old-street beggar. You, my friend, have a huge market value. YOU SMARTYPANTS PROGRAMMER!
SWAG
  • SWAG
http://blog.openstudy.com/wp-content/uploads/2012/06/Parth-SmartScore-Profile-copy.png
ParthKohli
  • ParthKohli
...?
ParthKohli
  • ParthKohli
That's a pretty old screenshot. :-)
SWAG
  • SWAG
Lol yeah i found it on google images
ParthKohli
  • ParthKohli
yeah, they had written a blog post on me. -_-
SWAG
  • SWAG
Yeah I see its about how young you are haha
Opcode
  • Opcode
@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
  • ParthKohli
@SWAG It's about how young and stupid I am. :-)
ParthKohli
  • ParthKohli
@Opcode No! There are people much better than me: @DLS and @shubhamsrg
experimentX
  • experimentX
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.
ParthKohli
  • ParthKohli
Wow, you could do trig?! WOW!
experimentX
  • experimentX
simple trigonometry ... that's the best i could do.
Opcode
  • Opcode
Pssh, tell the truth: Look at Parth: http://blog.openstudy.com/2012/06/27/our-youngest-user-and-quickest-to-99/ I can do simple trigonometry... :3 Parth taught me the basics :P I found the rest by internet :D
shubhamsrg
  • shubhamsrg
Juzt sho berry Amaysing! :O I am going to create a parth kohli fan club on facebook now.
Opcode
  • Opcode
Yush ^_^. I need to start using Facebook more anyway :-) Onward!
ParthKohli
  • ParthKohli
...
shubhamsrg
  • shubhamsrg
(Y)
Opcode
  • Opcode
Just a joke Parth :-) I'm wasting away in class :| I really should be listening >.>
shubhamsrg
  • shubhamsrg
http://www.facebook.com/groups/499948566734706/
Opcode
  • Opcode
Not joining that group... When Parth says "..." It means --> No. Just No. *Any then the Parth meme was born :O*
ParthKohli
  • ParthKohli
Proceed, my child.
Opcode
  • Opcode
Boop ^.^ http://cdn.memegenerator.net/instances/400x/35373413.jpg
ParthKohli
  • ParthKohli
Don't. Start. Parth. Kohli. Memes. I'm. Not. Chuck. Norris.
shubhamsrg
  • shubhamsrg
Well I don;t dare to offend The Parth Kohli.
shubhamsrg
  • shubhamsrg
My apologies.
Opcode
  • Opcode
Opcode promises this is the last one: http://cdn.memegenerator.net/instances/400x/35373583.jpg Now back to studying -_-
shubhamsrg
  • shubhamsrg
http://gyazo.com/73d47564ed85f1b06dcf4d05f3a8eae6
Opcode
  • Opcode
Would you like a shubhamsrg meme :3
shubhamsrg
  • shubhamsrg
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.
Opcode
  • Opcode
Next time if anyone calls you dumb use the ParthKohli defense!
shubhamsrg
  • shubhamsrg
ofcorse , as I said, I am gonna show him this screenshot! :)
shubhamsrg
  • shubhamsrg
Because when he says it, it can't be wrong!
shubhamsrg
  • shubhamsrg
Not that I am agreeing what he is saying, but he has said it, so no one can argue.
Opcode
  • Opcode
Hmm. Can I possible get a Ph. D in history? Or is that a no?
shubhamsrg
  • shubhamsrg
Only one person can answer all the questions in the world! Yes thats right,! We all know who that is. ^_^

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