Checking Kirchhoff's current law

[Special One]

Homework Statement

Prove the law

Relevant Equations

KCL

Im trying to apply KCL to the serial c and parallel rl circuit.

IZ =

=

= 330.562 mA
but this means incorrect proof.
Anyone can help please?

 

[gneill]

Note the 2 Ω resistance in series with the inductor. The branch is not purely reactive in nature. The current through that branch will not be purely 90° out of phase with the current through the resistor branch.

Can you find the phase angle of the impedance of that branch?