What is the impedance of a tank circuit at resonance?

[drumercalzone]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I think I have part a:
Z = j({\omega}C - \frac{1}{{\omega}C})

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

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

This gives an impedance of \infty

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

 

[rude man]

Y = jwC - j/wL = j(wC - 1/wL) = j(w^2LC - 1)/wL

Z= 1/Y = jwL/(1 - w^2LC)