Algebra help with complex numbers

[iScience]

Homework Statement

goal: solve for t; all else are constants

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

Homework Equations

none

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..

 

[LCKurtz]

Homework Statement

goal: solve for t; all else are constants

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

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

 

[Ray Vickson]

Homework Statement

goal: solve for t; all else are constants

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

Homework Equations

none

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..

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.

 

[Joffan]

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