Trig help.. electricity.. help

Find the combined impedance of the circuit elements in the figure below. The frequency of the current is 75 Hz.

35 Ω

95 μF 45 mH

First find the inductive reactance, then the capacitive reactance
Xl = 2*π*f*L = 21.21 ohms, this is j21.21 ohms
Xc = 1/(2*π*f*C) = 22.34 ohms this is -j 22.34 ohms
Now are they in series?
If so
X = Xl - Xc = 21.21 - 22.34 = -1.13 ohms, this is -j1.13 ohms
Z = √(35^2 +(-1.13)^2) = 35.02 ohms, this is the magnitude of Z
at an angle w of tan^-1 (-1.13/35), w is -1.85 degrees, the actual impedance is nearly resistive
note the reactive impedance is -j1.13
so Z = 35 - j1.13 ohms

In Parallel? The analysis is more complicated
if so
X p = Xl*(-Xc)/(Xl - Xc) = 419.32 ohms, this is j 419.32 ohms
Z = R*(jXp)/(R + jXp) =j14,760/(35 +j419.32)= 34.88 ohms at an angle of 4.8 degrees, this is nearly resistive

Are they in series?

Capacitive Reactance Xc = 1/(2πfC)
Inductive Reactance Xʟ = 2πfL
Impedance Z = √(R² + X²)
where X = Xʟ – Xc

Xc, Xʟ, Z are in Ω, f is in Hz
C in farads, L in Henrys

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