Impedence of 90° out of phase Capacitor and Inductor in parallel
While it may seem counter-intuitive, a parallel combination an inductor and capacitor will behave like an open circuit where their impedances match; even more counter-intuitively, a series combination will appear like a dead short under such conditions!

Essentially what happens is that in the parallel case, any voltage which is applied will cause equal and opposite (relative to the applied voltage) currents to flow in the capacitor and inductor, so all current that flows through the inductor will also flow through the capacitor in a loop, without any current flowing through the source of the applied AC voltage.

In the series case, any current which flows through the inductor will also flow through the capacitor; this will cause the voltage drop of each device to be precisely cancelled out by the other, so the net voltage drop across the series string will be precisely zero.

Note that these precise cancellations only happen at the resonant frequency of the LC combination.  At other frequencies, the effects of one or the other component will dominate.