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Homework Help: Help with Eulers relation in Fourier analysis

  1. Apr 14, 2013 #1
    Hi I'm doing fourier analysis in my signals and system course and i'm looking at the solution to one basic problem but I'm having trouble understanding one step
    Can anyone explain to me why
    From Eulers formula: http://i.imgur.com/1LtTiKX.png

    for example the Cosine in my problem. I thought the "twos" would cancel each other but instead becomes 4 and simular for the sine.
  2. jcsd
  3. Apr 14, 2013 #2


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    [tex]\cos z = \frac{e^{jz} + e^{-jz}}{2}[/tex]
    then multiply everything by 2 to get
    [tex]2 \cos z = e^{jz} + e^{-jz}[/tex]

    Or you can use the identity
    [tex]e^{jz} = \cos(z) + j \sin(z)[/tex]
    and also immediately get
    [tex]e^{jz} + e^{-jz} = \cos(z) + j \sin(z) + \cos(z) - j \sin(z) = 2 \cos(z)[/tex]
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