simplify this...

Discussion in 'Math' started by jut, Mar 27, 2009.

  1. jut

    Thread Starter Senior Member

    Aug 25, 2007
    224
    2
    e^{(-1+2j)t}+e^{(-1-2j)t}


    my attempt:
    e^{-t}e^{j2t} + e^{-t}e^{-j2t}

    e^{-t}(e^{j2t} + e^{-j2t})

    euler's identity says...

    cos(2t)=e^{j2t}+e^{-j2t}/2

    so...

    e^{(-1+2j)t}+e^{(-1-2j)t} = e^{-t}(2cos(2t))

    it seems right, but it's wrong! I checked the proof by substituting numbers into the original equation and the final equation and they evaluate to different numbers. :(

    Any help would be nice.
     
    Last edited: Mar 27, 2009
  2. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    jut,

    Your solution is correct, but your substitution is wrong. I plotted both the given expression and your solution. They were identical.

    Ratch
     
  3. jut

    Thread Starter Senior Member

    Aug 25, 2007
    224
    2
    Thanks. OK the solution was correct. I must have goofed up the substitution last night.

    Strangely enough, MATLAB simplified the expression to: 2*exp(-1)*cos(2*t)
    which was very close.
     
    Last edited: Mar 27, 2009
  4. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    jut,

    I disagree with both MATLAB and your assessment. 2*exp(-1)*cos(2*t) = 2*0.37*cos(2t) is a constant amplitude sinusoidal wave. The correct solution is an exponentially damped sinusoidal wave.

    Ratch
     
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