ParthKohli Group Title 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

1. ParthKohli Group Title

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

2. ParthKohli Group Title

Well, we essentially want to show that $$\pm i,\pm 1\; |\; 1$$ and they are the only ones.

3. ParthKohli Group Title

But how will I show that they are the only ones?

4. ParthKohli Group Title

@Opcode and @experimentX any ideas?

5. experimentX Group Title

No .. have to see.

6. ParthKohli Group Title

Well... $$a^2 + b^2 = 1$$

7. experimentX Group Title

I think you don't mean http://en.wikipedia.org/wiki/Gaussian_units you mean http://en.wikipedia.org/wiki/Gaussian_integer

8. ParthKohli Group Title

I mean Gaussian units. See my first post

9. Opcode Group Title

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

10. experimentX Group Title

looks like there is solution on M.SE http://math.stackexchange.com/questions/108071/unique-units-of-gaussian-integers

11. ParthKohli Group Title

OK yeah, I mean that they are a unit.

12. experimentX Group Title

units of Gaussian Integer ... looks like related to ring theory.

13. ParthKohli Group Title

ah! nice

14. Opcode Group Title

What math is this? I see on the MSE thing it says: abstract-algebra, ring-theory. So is it both?

15. ParthKohli Group Title

Ring theory is a subset of abstract algebra. This is theoretical mathematics also known as pure mathematics.

16. Opcode Group Title

What would you even need this for? Like job wise?

17. ParthKohli Group Title

@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 Group Title

@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 Group Title

@experimentX Can we call this complex analysis?

20. Opcode Group Title

Ouch. So much things to learn -_- If I was to attempt to get a Ph. D I'd be at age 40 :(.

21. experimentX Group Title

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 Group Title

I think abstract algebra is at more fundamental level than complex analysis.

23. Opcode Group Title

How old are you experimentX? (If I may ask?)

24. experimentX Group Title

celebrating 25th spring

25. Opcode Group Title

Wow. You guys are so smart! I feel so dumb around you guy :(

26. experimentX Group Title

Just below average old guy!! There is nothing wow about me ... Looks like parth will grow up to be smart guy.

27. Opcode Group Title

Yes, very smart indeed. @ParthKohli you education is so beautiful :-)

28. ParthKohli Group Title

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 Group Title
30. ParthKohli Group Title

...?

31. ParthKohli Group Title

That's a pretty old screenshot. :-)

32. SWAG Group Title

Lol yeah i found it on google images

33. ParthKohli Group Title

yeah, they had written a blog post on me. -_-

34. SWAG Group Title

Yeah I see its about how young you are haha

35. Opcode Group Title

@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 Group Title

@SWAG It's about how young and stupid I am. :-)

37. ParthKohli Group Title

@Opcode No! There are people much better than me: @DLS and @shubhamsrg

38. experimentX Group Title

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 Group Title

Wow, you could do trig?! WOW!

40. experimentX Group Title

simple trigonometry ... that's the best i could do.

41. Opcode Group Title

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 Group Title

Juzt sho berry Amaysing! :O I am going to create a parth kohli fan club on facebook now.

43. Opcode Group Title

Yush ^_^. I need to start using Facebook more anyway :-) Onward!

44. ParthKohli Group Title

...

45. shubhamsrg Group Title

(Y)

46. Opcode Group Title

Just a joke Parth :-) I'm wasting away in class :| I really should be listening >.>

47. shubhamsrg Group Title
48. Opcode Group Title

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

49. ParthKohli Group Title

Proceed, my child.

50. Opcode Group Title
51. ParthKohli Group Title

Don't. Start. Parth. Kohli. Memes. I'm. Not. Chuck. Norris.

52. shubhamsrg Group Title

Well I don;t dare to offend The Parth Kohli.

53. shubhamsrg Group Title

My apologies.

54. Opcode Group Title

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

55. shubhamsrg Group Title
56. Opcode Group Title

Would you like a shubhamsrg meme :3

57. shubhamsrg Group Title

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 Group Title

Next time if anyone calls you dumb use the ParthKohli defense!

59. shubhamsrg Group Title

ofcorse , as I said, I am gonna show him this screenshot! :)

60. shubhamsrg Group Title

Because when he says it, it can't be wrong!

61. shubhamsrg Group Title

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

62. Opcode Group Title

Hmm. Can I possible get a Ph. D in history? Or is that a no?

63. shubhamsrg Group Title

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