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Algebra question?

  1. Oct 7, 2005 #1
    Note:
    It looks like the LaTeX interpreter is not working right now. So I'll try and use plaintext and make things look pretty.

    To my problem:
    My algebra skills are kind of weak, but I am trying to show the Laplace transform of cos(at) and I keep getting stuck at this one spot.

    it is where
    L{e^(i*a*t)} = 1/(s+i*a)

    How do I get the complex part out of the bottom? My TI-89 will do it for me automatically... but I can't just turn the solution in like that :)
    So the TI-89 says that:

    Code (Text):

     1           s           a
    ----   = --------- + --------- i
    s+ia      s^2+a^2    s^2+a^2
     
    (or if LaTeX starts working again)
    [tex]
    \frac{1}{s+ia}=\frac{s}{s^2+a^2}+\frac{a}{s^2+a^2}*i
    [/tex]

    So how the hell is my calc doing that?... partial fractions maybe? I dunno... and it is friggn' bugging me. Thanks in advance.

    Sorry about the ascii art :)
     
  2. jcsd
  3. Oct 7, 2005 #2

    siddharth

    User Avatar
    Homework Helper
    Gold Member

    Multiply numerator and denominator by (s-ia).
    So you will get
    s/(s^2+a^2) -ia/(s^2+a^2)
     
  4. Oct 7, 2005 #3
    that was easy :smile:

    thank you !
     
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