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Quick question on Euler's Theorem

  1. Dec 2, 2007 #1
    Ok, in my diffeq book, we're doing work on getting eigenvectors to complex eigenvalues.

    anyway the author of the book only mentions Euler's Theorem as: http://rogercortesi.com/eqn/tempimagedir/eqn5095.png [Broken]
    and so he perfers to work with http://rogercortesi.com/eqn/tempimagedir/eqn7868.png [Broken] when the roots are eqn3362.png

    So my question:

    What is this called then?: eqn9909.png
    and can i use in place for eqn4478.png and still call it Euler's Theorem?
     
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Dec 2, 2007 #2

    Dick

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    It's called "Euler's theorem with -t substituted for t after applying the identity sin(-t)=-sin(t)". Does it really need a name?
     
  4. Dec 4, 2007 #3
    Thx for that. I was sorta expecting some kind of identity to do that.
     
    Last edited: Dec 4, 2007
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