The relevant circuit is shown below,
We should first find the complex power delivered by the independent source. I derived it but my answer was different than the answer given. So, I am wondering where I went wrong. My work is,
First thing we have to do is find \$V_x\$. We can see that the current through the inductor is \$\dfrac{V_x}{j}\$ so the current through the capacitor is then \$5cis(30)-\frac{V_x}{j}\$. Thus, the current in the 2 ohm resistor by KCL is \$5cis(30)-\frac{V_x}{j} +2V_x\$. Then doing KVL around the whole loop we get,
\$-V_x-j(5cis(30)-\frac{V_x}{j})+2(5cis(30)-\frac{V_x}{j} +2V_x)=0\$
Solving the equation for \$V_x\$, $$V_x= \frac{5cis(120)-10cis(30)}{3+3j}$$ $$ S=V_xI^{*}$$ And to find the complex power we need only multiply by the conjugate of the current which is \$5cis(-30)\$ to get a final answer, \$-4.2 +12.5j\$ which is different than the given answer. Is my work wrong? I would appreciate it if someone can point out the mistake and/or offer a correction.