Determine the numerical value of the current through the capacitor by whatever method you prefer.
Nodal analysis is pleasant enough. Mesh analysis is also not too bad...
Nodal Analysis
Ground the bottom node.
Multiplying through by j20 yields:
Thus the current through the capacitor is:

Mesh Analysis
Mesh 1:
Simplifying slightly:
Multiplying the second equation by 2 and
Thus the current in the first mesh is zero; from equation 2:
The current through the capacitor is I_{1}  I_{2}, so

Very interesting! There is no current flow through the 10 V source??? It's very happy though...
Thevenin Analysis
If you are a Thevenin enthusiast, then your generator should consist of a voltage source of 5.94 V \/ 16.8 deg and an impedance of 1.86 ohm \/ 68.2 deg. Full speed ahead...
Thanks go to Chris Lane (Fall 1999) for pointing out an important typographical error in the original solution.