The impedance Z = R -j/wC + ##\frac{1}{\frac{1}{R} - \frac{\omega C}{j}}##
But,1/wC=R
So, solving this, I find:
Z= 3R/2(1-j)
|Z| =##\frac{3R}{\sqrt 2}##
I =##\frac{V_i \sqrt 2} {3R}##
Vi - IR-IXc =Vo
Solving this,
##Vo = V_i -\frac {V_i \sqrt 2}{3} - \frac{V_i \sqrt 2}{3R} \frac{-j}{wC}##...