Intelligent Maths Minds needed

Discussion in 'Community' started by JLS, Nov 17, 2004.

  1. JLS macrumors 6502

    Joined:
    Aug 8, 2004
    Location:
    Kent, England
    #1
    My friend is totally stuck with a couple of problems, and doesn't know where to start. If anyone could post anything to help him get started, I would appreciate it greatly - and so would he. :)

    Thanks

    [​IMG]
     
  2. raiderz182 macrumors regular

    Joined:
    Oct 17, 2003
    Location:
    north philly
    #2
    i wish i could help, damnit! i just did this 2 months ago too....
     
  3. dotnina macrumors 6502a

    Joined:
    Aug 19, 2004
    #3
    Oh dear. I took a class on complex analysis, and right around the time we started doing this, I dropped the class. :(

    If it's a problem out of a textbook, try Googling for something like

    site:.edu +"de moivre" +[author's last name]

    Sometimes you can find the syllabus of some class this way, and sometimes that'll lead you to good lecture notes. Other than that ... I got nothin'.
     
  4. atszyman macrumors 68020

    atszyman

    Joined:
    Sep 16, 2003
    Location:
    The Dallas 'burbs
    #4
    Start the first one by breaking it into Euler's identity

    cos(Ø) = 1/2 (e^jØ + e^(-jØ))

    so

    (cos(Ø))^5 = (1/2 (e^jØ + e^(-jØ)))^5

    From there you can start doing expansions/simplifications. This should help get you to de Moivre's a bit easier since

    e^jØ = cos(Ø)+j*sin(Ø)

    Can't necessarily provide any guidance on the others though.

    Edit: You would probably be more familiar with using i = (-1)^(1/2) rather than j which I used. Electrical Engineers just have to be different.
     
  5. Mr. Anderson Moderator emeritus

    Mr. Anderson

    Joined:
    Nov 1, 2001
    Location:
    VA
    #5
    Never did really understand that, given that its an imaginary number, so 'i' fits - does 'j' stand for anything or is it just random?

    D
     
  6. atszyman macrumors 68020

    atszyman

    Joined:
    Sep 16, 2003
    Location:
    The Dallas 'burbs
    #6
    It's because early on in circuit analysis you learn
    P = power
    I = current
    V or E = voltage

    There are certain meanings between DC and AC with uppercase and lowercase letters. So rather than have i = DC current or (-1)^(1/2) it's easier to use j for imaginary numbers to avoid confusion. Why j was chosen I'm not entirely sure, my guess is partly because it's the next letter in the alphabet, also possibly because a lowercase j looks a lot like lowercase i.
     
  7. Abstract macrumors Penryn

    Abstract

    Joined:
    Dec 27, 2002
    Location:
    Location Location Location
    #7
    I tried to understand maths using "imaginary" numbers, but then I realized that I was just imagining them and moved on.
     
  8. stubeeef macrumors 68030

    stubeeef

    Joined:
    Aug 10, 2004
    #8
    I couldn't get it to get through spell check!

    Sorry.
     
  9. celaurie macrumors 6502a

    celaurie

    Joined:
    Mar 2, 2003
    Location:
    Edinburgh, Scotland.
    #9
    ~Duh

    Isn't it an Egyptologist you need for hieroglyphics? :rolleyes:

    ~cel, no one ever said he had a clue
     
  10. Hoef macrumors 6502a

    Hoef

    Joined:
    Jul 11, 2004
    Location:
    Houston, TX..... (keep walking)
    #10
    Argh... six years of electrical engineering and totally forgot how to do this. Punished for being a consultant for 6 years. Good luck though!
     
  11. atszyman macrumors 68020

    atszyman

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    Sep 16, 2003
    Location:
    The Dallas 'burbs
    #11
    Another tip. In doing the expansion remember that sin^2+cos^2 = 1
     
  12. jimsowden macrumors 68000

    jimsowden

    Joined:
    Sep 6, 2003
    Location:
    NY
    #12
    I'm not sure if this has anything to do with Trig, which it almost certainly doesn't, but remember the law of sines and cosines:
    a/sinA=b/sinB=c/sinC and a^2=b^2+c^2-2bccosA
    and so on.
     
  13. atszyman macrumors 68020

    atszyman

    Joined:
    Sep 16, 2003
    Location:
    The Dallas 'burbs
    #13
    Ask me a year ago and I couldn't have told you how to get started either. But 15 credits into my Masters it is starting to become old hat.
     
  14. atszyman macrumors 68020

    atszyman

    Joined:
    Sep 16, 2003
    Location:
    The Dallas 'burbs
    #14
    I used to think that, but after 9-12 credits of signal processing classes imaginary numbers have all kinds of practical uses. One of which being if you build the right load you could theoretically plug it into your wall and drop your electric bills to zero. But I believe that is slightly illegal.
     
  15. KingSleaze macrumors 6502

    Joined:
    Feb 24, 2004
    Location:
    So. Cal
    #15
    And in practical terms, you couldn't do it. Perpetual motion would be just as easy.
     
  16. atszyman macrumors 68020

    atszyman

    Joined:
    Sep 16, 2003
    Location:
    The Dallas 'burbs
    #16
    Darn it. I had a good reply all typed up and then I did some research.

    I was wrong, you can reduce your power bills but not eliminate them, but it is not that hard to do. It merely requires correcting the inductive load of your home/business by adding capacitance until the load appears purely resistive.

    On a side note-

    After staying up late doing homework (lots of imaginary numbers) and dealing with our 8 day old daughter earlier this week. I was greatly disturbed on Tuesday morning when my snooze button only dealt with real time and didn't account for the imaginary part... I really need more sleep.
     

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