Impedance as a function of angular frequency

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

2. Relevant equations
Z_L = jωL
Z_C = 1/(jωC) = -j/(ωC)

3. The attempt at a solution

This is my attempt for the series combination:

Z = jωL + 1/(jωC)
Z = j0.02ω – j20000/ω

Is there a way to simplify this further? What would a graph look like, if the function has imaginary parts?

And also, to find the frequency for an equivalent open circuit, I would have to set the impedance to zero right? What would it be for a short circuit?
^EDIT: Actually I just realized that I would set Z equal to zero for a short circuit, not an open circuit.
For an open circuit, the impedance should be infinite, but how would I find the angular frequency?
∞ = j0.02ω – j20000/ω does not seem like a solvable equation.

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