In the accompanying phasor diagram, the resistance of theresistor, R, is represented by the red horizontal vector drawn along the positive real axis of the Z-plane.
The capacitor, C, is represented by the blue vertical vector drawn downward along the negative reactance axis of the Z-plane. Its reactance is negative by an amount given by the negative reciprocal of the product of the angular frequency and the capacitance, C, of the capacitor.
The diagonal purple impedance vector is the vector sum of the resistance vector (red), and the capacitive reactance vector (blue). Its magnitude (length) and angle (theta) are calculated from simple geometric laws, using the pythagorean theorem, and simple trigonometry. If the input is a steady state sinusoidal waveform, the impedance, Z, is the impedance that is imposed across the input waveform.
The output waveform, also sinusoidal, will differ in magnitude and phase angle from the input sinusoid. As in a simple voltage divider circuit the magnitude of the output is determined as the ratio of the length of the red vector, R, to the magnitude (length) of the purple vector, Z, and the phase angle difference (theta) between the output sinusoid and the input sinusoid is determined by the arctangent function.
As frequency increases, the head of the purple impedance vector rises along the vertical dotted line, and one can easily visualize the changes in the impedance magnitude ratio as well as the phase angle (theta).