# Algebra help with complex numbers

1. Nov 10, 2014

### iScience

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. Nov 10, 2014

### LCKurtz

If you know values for $R,~C,~\omega$ you can solve it numerically. Otherwise you are out of luck.

3. Nov 10, 2014

### Ray Vickson

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.

4. Nov 11, 2014

### Joffan

Just looking at the form of the original equation, how many solutions do you expect and roughly where?