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Question about cosine and Eulers identity

  1. Jul 5, 2009 #1
    I was doing a signals and systems problem and I think I might be screwing something up with the cosine function because I get

    [tex]cos(a+b) = cos(a)*cos(b)[/tex]

    This is how

    [tex]cos(a+b)=Re\left\{ e^{j*(a+b)} \right\}[/tex]
    [tex]=Re\left\{ e^{j*(a)}*e^{j*(b)} \right\}[/tex]
    [tex]=cos(a)*cos(b)[/tex]

    Can anyone point out my mistake?

    EDIT:
    I guess I figured it out. The Re{} function isn't distributive. Thanks for your time.
     
  2. jcsd
  3. Jul 5, 2009 #2
    The expression at the second to last line will involve a multiplication of two factors each having one j (imaginary unit), which results in the missing real expression.
     
  4. Jul 5, 2009 #3
    In simpler language... the real part of a product is not the product of the real parts
     
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