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## Homework Statement

[Edit: Sorry for the typo in the thread title]

I'm doing a problem that involves taking the derivative of the impedance of a parallel RLC circuit with respect to the frequency ω of the applied voltage. I have to then set that derivative equal to zero to find the frequency at which the maximum impedance occurs. I'm pretty sure I did everything mostly right, but my answer ended up being imaginary. I ended up with ω = [itex]\frac{i}{\sqrt{LC}}[/itex]. I'm sure the coefficient is right, since that's the resonant frequency of the undamped circuit. But should it really be imaginary? That seems odd to me. I've never actually taken the derivative of anything involving i before, so there might be something different you have to do that I don't know about. Anyway, I'm going to post my work. If someone could point out where I messed up (or explain why it's okay for the answer to be imaginary) it would be greatly appreciated. Thanks!

## Homework Equations

Z = [itex]\frac{1}{\frac{1}{R}+iωC -\frac{i}{ωL}}[/itex]

## The Attempt at a Solution

[itex]\frac{dZ}{dω} = -1(\frac{1}{R}+iωC -\frac{i}{ωL})^{-2}(iC+\frac{i}{ω^{2}L}[/itex])

-iC-[itex]\frac{i}{ω^{2}L}[/itex] = 0

[itex]ω^{2} = \frac{-1}{LC}[/itex]

ω = [itex]\frac{i}{\sqrt{LC}}[/itex]

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