How to Apply Nodal Analysis in the Phasor Domain to Determine ix(t)?

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Homework Statement

Apply nodal analysis in the phasor domain to determine ix(t) in the circuit below.

Homework Equations

The Attempt at a Solution

This is super confusing to calculate in the phasor domain, I was just wondering if anyone could check my calculations and see if they get the same answer that I do.

 

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Here is my attempt