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)