Solution - Semi-infinite RLC Circuit

See picture above. Because the circuit is semi-infinite, total impedance of circuit in the box is the same with total impedance of the whole circuit. So we can draw the circuit like picture below.
To make it easier, we should work with complex number.
Hence, the impedance of resistor, inductor, and capacitor are respectively

So the total impedance of the circuit is

Substitute the impedance of resistor, capacitor, and inductor at the equation above.

Solve the equation for Ztot, and we get

And now we need to change the form, so we assume that

Then give the power of two for each sides of the equation.

And now we can get

and

Solving these equation, and we get

So the total impedance is

Because the real part of impedance cannot be negative, so the total impedance is

So, the magnitude of total impedance is

That's my solution.
If you have any question, correction, or comment, please leave a comment below.
Thank you.