s=R/w^4L^2C^2+j(2/wc-1/w^3LC^2)
if the imaginary term equates to 0, show that the equation can be written as R=S/4
Hello
We have $\displaystyle
S=\frac{R}{\omega^4L^2C^2}+\jmath\left( \frac{2}{\omega C}-\frac{1}{\omega^3 LC^2}\right)$ and we know that the imaginary part of $\displaystyle S$ equals 0. It gives an equation : $\displaystyle \frac{2}{\omega C}-\frac{1}{\omega^3 LC^2}=0$ from which you can get the value of $\displaystyle \omega$. (hint : factor by $\displaystyle \frac{1}{\omega C}$ to solve this equation) Once you've found $\displaystyle \omega$ you're done since $\displaystyle S=\frac{R}{\omega^4L^2C^2}=\ldots$
You can treat it as a normal sum of fractions : bring the two fractions to the same denominator and then solve $\displaystyle \text{numerator}=0$. You can also follow the hint I've given : factoring by $\displaystyle \frac{1}{\omega C}$ should give you two equations (one of which has no solutions) which can be solved for $\displaystyle \omega$.