Electronic – Estimated impedance of a 12V bleeper

Diagram!

This is for a complex impedance:

\$Z = R + \dfrac{1}{j \omega C} \$

Resistance \$R\$ is in phase with the applied voltage, so the vector points in the same X direction. The impedance of a capacitor is almost completely reactive, i.e. its resistive part is much smaller than the \$\dfrac{1}{j \omega C} \$. The \$j\$ causes a \$\theta\$ = 90° rotation, and since the \$j\$ (= \$\sqrt{-1}\$) is in the denominator the angle is negative \$\left( \dfrac{1}{j} = -j \right) \$.
To calculate the current \$ I = \dfrac{U}{Z} \$, we note that when dividing by an impedance with angle \$\theta\$ we subtract the angle from our reference, so that the angle's sign is inverted.
The result shows how for a capacitive load the current leads the voltage by an angle \$ \theta\$, where \$ 0 \le \theta \le 90°\$.
For inductive loads a similar diagram can be drawn, only \$ j \omega L\$ points in the opposite direction of \$\dfrac{1}{j \omega C} \$, and the current will trail the voltage.

edit (after your edit of the question)
So, resistance will cause the current to be in phase with the voltage. If there's an imaginary term (the \$j\$) then that term represents the reactance, either capacitive or inductive, and

Resistance + Reactance = Impedance

In an ideal world, if you don't have capacitors or coils you wouldn't have reactance either. But a circuit may have parasitic impedance: the length of a PCB trace will cause an inductive reactance (it behaves as a coil), and two adjacent traces will have a capacitive reactance (they behave as a capacitor). Parasitic impedances are unintentional, and most of the time a nuisance, though sometimes a designer can make good use of them.
You can measure components impedances with an RLC-meter, which will give you resistance in series or parallel with a reactance (inductive or capacitive).
Reactance will show as a phase shift in voltage or current. This phase shift can be shown on an oscilloscope in X-Y mode; a zero phase shift will show a straight line, a 90° phase shift will show a circle, anything in between will give you an ellipse.

Why don't you just use the circuit design recommended by the buzzer manufacturer in their data sheet. I.E. this circuit:

This uses a simple CD4049 chip, two resistors and a small capacitor. This curcuit gives you the gain you need to make the oscillation work.