AC Circuit Analysis- Find Impedance

[Valour549]

Homework Statement

2. The attempt at a solution

Am I doing something wrong? I know it's just voltage division with AC phasors and we have to equate the real parts and imaginary parts to find the unknown, but I feel like the question shouldn't be this hard.

 

[Dr.D]

How you feel is usually irrelevant. Are you satisfied with the answer? Did you check all your work?

 

[gneill]

I think you're making it more difficult than it has to be by starting with Z = R + jX, which essentially doubles the number of variables to deal with.

Instead, I would suggest writing Nodal Analysis equations and solving for Z.

Since $V_o$ is already given, you can take advantage of that as that node is "solved" already.

Once you have complex Z you can split it into its R and X components.