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Algebra help with complex numbers

  1. Nov 10, 2014 #1
    1. The problem statement, all variables and given/known data

    goal: solve for t; all else are constants

    $$cos(\omega t)=1-e^{-(\frac{t}{RC})}$$


    2. Relevant equations

    none


    3. The attempt at a solution

    i turned the cos to complex notation & rearranged

    $$e^{i\omega t}+e^{-(\frac{t}{RC})}=1$$

    $$ln(e^{i\omega t}+e^{-(\frac{t}{RC})})=0$$

    and i am stuck..
     
  2. jcsd
  3. Nov 10, 2014 #2

    LCKurtz

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    If you know values for ##R,~C,~\omega## you can solve it numerically. Otherwise you are out of luck.
     
  4. Nov 10, 2014 #3

    Ray Vickson

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    No wonder you are stuck: ##e^{i \omega t} \neq \cos(\omega t)##. Besides that, I doubt very much that your equation possesses a closed-form solution. You will probably need to resort to approximations, or to numerical solutions for known numerical values of your input constants.
     
  5. Nov 11, 2014 #4
    Just looking at the form of the original equation, how many solutions do you expect and roughly where?
     
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