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Homework Help: Fourier series of exponential term

  1. Jan 10, 2010 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=22975&stc=1&d=1263150596.jpg


    2. Relevant equations



    3. The attempt at a solution
    Ive numbered the solution steps, the ones that are giving me trouble are from 1 to 2 and from 3 to 4

    From 1 to 2 i don't understand how there can be an exp(x) term taken out of the bracket and still be in the bracket, also don't know how the (1-in) and (1+in) can be taken out but still left in the exp() term

    And from 3 to 4 i am assuming its a trig identity but i can't find any on the internet so im not sure if theres an intermediate step in between these two of whether its a straight swap for an identity
     

    Attached Files:

  2. jcsd
  3. Jan 10, 2010 #2
    1-2

    multiply the nr and dr by complex conjugate of the dr and remove exp(x) which is a common factor

    3-4
    famous euler's equation
    exp(ix) = ........

    hope it helped
     
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