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## Homework Statement

## Homework Equations

$$ V=IR $$

## The Attempt at a Solution

To simplify the algebra it was suggested that I set $$ R_{1}=R_{2}=R $$ and $$C_{1}=C_{2}=C $$ So that's what I did. I labeled the voltage in the middle node as $$ V_{1} $$Taking KCL at the middle node gives $$ \frac{V_{s}-V_{1}}{R}-j\omega CV_{1}+\frac{V_{0}-V_{1}}{R} =0 $$ which simplifies to $$V_{1}=\frac{V_{s}+V_{0}}{2+jR\omega C} $$Then I took KCL at the rightmost node, giving $$V_{0}=\frac{V_{1}}{1+jR\omega C} $$ after simplification. Substituting my previous expression for $$ V_{1} $$ into the equation gives $$2+3jR\omega C-R^2\omega^2C^2=\frac{V_{s}+V_{0}}{V_{0}} $$After some more simplification. From here on I'm having trouble getting an answer out. I tried substituting in known values $$ \omega=2000, V_{s}=15, V_{0}=-j2 $$ and got some nonsensical equation with no solutions? I think the solution they (very briefly) explained involved transforming it to the polar form but I'm not seeing how that would simplify things. Any pointers will be greatly appreciated, thanks!