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ParthKohli

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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  1. ParthKohli
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    A Gaussian unit is a Gaussian integer \(z\) such that \(\dfrac{1}{z}\) is also a Gaussian integer.

    • one year ago
  2. ParthKohli
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    Well, we essentially want to show that \(\pm i,\pm 1\; |\; 1\) and they are the only ones.

    • one year ago
  3. ParthKohli
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    But how will I show that they are the only ones?

    • one year ago
  4. ParthKohli
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    @Opcode and @experimentX any ideas?

    • one year ago
  5. experimentX
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    No .. have to see.

    • one year ago
  6. ParthKohli
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    Well... \(a^2 + b^2 = 1\)

    • one year ago
  7. experimentX
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    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
  8. ParthKohli
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    I mean Gaussian units. See my first post

    • one year ago
  9. Opcode
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    Sorry! Opcode is still learning trigonometry. No "Gaussian units" for now :( Mabye @Hero ?

    • one year ago
  10. experimentX
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    looks like there is solution on M.SE http://math.stackexchange.com/questions/108071/unique-units-of-gaussian-integers

    • one year ago
  11. ParthKohli
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    OK yeah, I mean that they are a unit.

    • one year ago
  12. experimentX
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    units of Gaussian Integer ... looks like related to ring theory.

    • one year ago
  13. ParthKohli
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    ah! nice

    • one year ago
  14. Opcode
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    What math is this? I see on the MSE thing it says: abstract-algebra, ring-theory. So is it both?

    • one year ago
  15. ParthKohli
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    Ring theory is a subset of abstract algebra. This is theoretical mathematics also known as pure mathematics.

    • one year ago
  16. Opcode
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    What would you even need this for? Like job wise?

    • one year ago
  17. ParthKohli
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    @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

    • one year ago
  18. experimentX
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    @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
  19. ParthKohli
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    @experimentX Can we call this complex analysis?

    • one year ago
  20. Opcode
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    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
  21. experimentX
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    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.

    • one year ago
  22. experimentX
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    I think abstract algebra is at more fundamental level than complex analysis.

    • one year ago
  23. Opcode
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    How old are you experimentX? (If I may ask?)

    • one year ago
  24. experimentX
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    celebrating 25th spring

    • one year ago
  25. Opcode
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    Wow. You guys are so smart! I feel so dumb around you guy :(

    • one year ago
  26. experimentX
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    Just below average old guy!! There is nothing wow about me ... Looks like parth will grow up to be smart guy.

    • one year ago
  27. Opcode
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    Yes, very smart indeed. @ParthKohli you education is so beautiful :-)

    • one year ago
  28. ParthKohli
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    Aw, no! I will grow up to be some old-street beggar. You, my friend, have a huge market value. YOU SMARTYPANTS PROGRAMMER!

    • one year ago
  29. SWAG
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    http://blog.openstudy.com/wp-content/uploads/2012/06/Parth-SmartScore-Profile-copy.png

    • one year ago
  30. ParthKohli
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    ...?

    • one year ago
  31. ParthKohli
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    That's a pretty old screenshot. :-)

    • one year ago
  32. SWAG
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    Lol yeah i found it on google images

    • one year ago
  33. ParthKohli
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    yeah, they had written a blog post on me. -_-

    • one year ago
  34. SWAG
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    Yeah I see its about how young you are haha

    • one year ago
  35. Opcode
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    @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
  36. ParthKohli
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    @SWAG It's about how young and stupid I am. :-)

    • one year ago
  37. ParthKohli
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    @Opcode No! There are people much better than me: @DLS and @shubhamsrg

    • one year ago
  38. experimentX
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    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
  39. ParthKohli
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    Wow, you could do trig?! WOW!

    • one year ago
  40. experimentX
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    simple trigonometry ... that's the best i could do.

    • one year ago
  41. Opcode
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    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

    • one year ago
  42. shubhamsrg
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    Juzt sho berry Amaysing! :O I am going to create a parth kohli fan club on facebook now.

    • one year ago
  43. Opcode
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    Yush ^_^. I need to start using Facebook more anyway :-) Onward!

    • one year ago
  44. ParthKohli
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    ...

    • one year ago
  45. shubhamsrg
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    (Y)

    • one year ago
  46. Opcode
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    Just a joke Parth :-) I'm wasting away in class :| I really should be listening >.>

    • one year ago
  47. shubhamsrg
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    http://www.facebook.com/groups/499948566734706/

    • one year ago
  48. Opcode
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    Not joining that group... When Parth says "..." It means --> No. Just No. *Any then the Parth meme was born :O*

    • one year ago
  49. ParthKohli
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    Proceed, my child.

    • one year ago
  50. Opcode
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    Boop ^.^ http://cdn.memegenerator.net/instances/400x/35373413.jpg

    • one year ago
  51. ParthKohli
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    Don't. Start. Parth. Kohli. Memes. I'm. Not. Chuck. Norris.

    • one year ago
  52. shubhamsrg
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    Well I don;t dare to offend The Parth Kohli.

    • one year ago
  53. shubhamsrg
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    My apologies.

    • one year ago
  54. Opcode
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    Opcode promises this is the last one: http://cdn.memegenerator.net/instances/400x/35373583.jpg Now back to studying -_-

    • one year ago
  55. shubhamsrg
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    http://gyazo.com/73d47564ed85f1b06dcf4d05f3a8eae6

    • one year ago
  56. Opcode
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    Would you like a shubhamsrg meme :3

    • one year ago
  57. shubhamsrg
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    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
  58. Opcode
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    Next time if anyone calls you dumb use the ParthKohli defense!

    • one year ago
  59. shubhamsrg
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    ofcorse , as I said, I am gonna show him this screenshot! :)

    • one year ago
  60. shubhamsrg
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    Because when he says it, it can't be wrong!

    • one year ago
  61. shubhamsrg
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    Not that I am agreeing what he is saying, but he has said it, so no one can argue.

    • one year ago
  62. Opcode
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    Hmm. Can I possible get a Ph. D in history? Or is that a no?

    • one year ago
  63. shubhamsrg
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    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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