1. The problem statement, all variables and given/known data

a) Determine the impedance of this circuit.
b) What is the impedance when [itex] \omega = \frac{1}{\sqrt{LC}} [/itex]

2. Relevant equations

3. The attempt at a solution

EDIT: I got the Z wrong. It's [tex] Z = \frac{L}{C(j{\omega}L - \frac{j}{{\omega}C})} [/tex]

[STRIKE]For part b, I'm getting that Z = 0 simply by substituting in [itex]\omega[/itex].
Is this correct? [/STRIKE]

This gives an impedance of [itex]\infty[/itex]

I feel more confident is this answer. I'm guessing that the current in the capacitor and inductor are out of phase by [itex]\pi[/itex] causing what appears to be an infinite impedance. I'm still curious as to the exact reason though, if anyone could lend help. Thanks!