Engineering Complex number help (AC circuit)

[Color_of_Cyan]

Homework Statement

Use the supernode technique to find I₀ in the circuit

Homework Equations

nodal analysis, AC analysis

The Attempt at a Solution

Taking the left essential node as V1 and the right essential node as V2,


V1 + 12V = V2

and

-V1/(1-1j)Ω + -V1 / 2Ω = V2 / 2jΩ + V2 / (2+2j)Ω


Then

(-2ΩV1 - 1ΩV1 + 1jΩV1)/(2-2j)Ω = 2ΩV2 + 4ΩjV2/(-2+4j)Ω


And sorry to say, but need help in knowing the best way to isolate v1 or v2 from here...

 

[gneill]

For nodal analysis using the supernode technique, there's really only one node in this circuit: the supernode itself. All the other nodes are embedded in series-connected branches wherein you can simply combine the impedances.