What is the magnitude of the impedance of a series RLC circuit at resonance?

The formula for total impedance (Z) in a series RLC circuit is Z = √(R² + (X_L - X_C)²), where R is resistance, X_L is inductive reactance, and X_C is capacitive reactance. By definition, at the resonant frequency, the inductive reactance and capacitive reactance are perfectly equal (X_L = X_C). Because they are equal but opposite in phase, they completely cancel each other out in the equation. With the reactive components effectively at zero, the formula simplifies to Z = √(R²), which means the total impedance Z is simply equal to the pure circuit resistance R.