Determining the resonant angular frequency
Impedance of 2 parallel (//) branches is easier to add the inverse or admittance,Y

\$Z(\omega )=(R+j\omega L) // (1 / j\omega C) \$ 

or 
\$Y(\omega )=\frac{1}{ Z(\omega )}=\frac{1}{R+j\omega L} +  \frac{j\omega C}{1} \$ 

to find resonance, differentiate \$df(\omega )/d(\omega )=0\$

if \$Y(\omega) = \frac{1+j\omega C(R+j\omega L)}{R+j\omega L} \$, then \$Y'(\omega) =... \$