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ParthKohli

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

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

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

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

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

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

  7. experimentX
    • one year ago
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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

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

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

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

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

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

  13. ParthKohli
    • one year ago
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    ah! nice

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

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

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

  17. ParthKohli
    • one year ago
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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

  18. experimentX
    • one year ago
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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.

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

  20. Opcode
    • one year ago
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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 :(.

  21. experimentX
    • one year ago
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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.

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

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

  24. experimentX
    • one year ago
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    celebrating 25th spring

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

  26. experimentX
    • one year ago
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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.

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

  28. ParthKohli
    • one year ago
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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!

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

  30. ParthKohli
    • one year ago
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    ...?

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

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

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

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

  35. Opcode
    • one year ago
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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 :-)

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

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

  38. experimentX
    • one year ago
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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.

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

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

  41. Opcode
    • one year ago
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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

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

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

  44. ParthKohli
    • one year ago
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    ...

  45. shubhamsrg
    • one year ago
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    (Y)

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

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

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

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

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

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

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

  53. shubhamsrg
    • one year ago
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    My apologies.

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

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

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

  57. shubhamsrg
    • one year ago
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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.

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

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

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

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

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

  63. shubhamsrg
    • one year ago
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    Only one person can answer all the questions in the world! Yes thats right,! We all know who that is. ^_^

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