Getting the numerical value of a capacitor's impedance
Your equations look right (did not break out pencil and paper but just inspecting), when you solve for an impedance. You will get a real and imaginary part, just drop the \$j\$ on the imaginary part, and solve for \$C\$ using an omega (the capacitance you seek will depend on the frequency of operation since \$\omega =2\pi f\$)