How Do I Combine Capacitor and Inductor Impedances in Parallel?

[swooshfactory]

Homework Statement

How do I combine these into an equivalent impedence? I'm dealing with complex impedence, but I'm not sure how to make them into an equivalent impedence.

Homework Equations

The Attempt at a Solution

I guess Zeq= 1/[(1/Zc)+(1/ZL)].
Is this right?

 

[swooshfactory]

Or do I replace the capacitor by an open circuit and inductor by a short?

 

[skeptic2]

I guess Zeq= 1/[(1/Zc)+(1/ZL)].
Is this right?

It looks pretty good to me, however I'd like to clarify a little terminology.

Z represents a complex value called impedance with both real and imaginary parts. Often however it is given as a single number which represents just the magnitude without the angle. As magnitude it is always positive.

Zc & ZL aren't correct because those values are always imaginary with no real part. Instead, the term X is used and it's called reactance.

Capacitive reactance (Xc) is always negative and Inductive reactance (XL) is always positive.

With no real parts the formula would be Xeq = 1/[(1/Xc) + (1/XL)].