Polar form vs phasor form?
A phasor is a complex representation of the magnitude and phase of a sinusoid and is based on Euler's identity:

$$ e^{\pm j\phi} = cos(\phi) \pm j sin(\phi) $$

If you have a sinusoidal voltage given by: $$ v(t) = V_m cos(\omega t + \phi)$$
you can express it in phasor form by first taking the real part of it

$$v(t) = Re(V_me^{j(\omega t + \phi)})$$
thus 
$$v(t) = Re(V e^{j\omega t})$$
where
$$V = V_m e^{j\phi} = V_m \angle \phi$$

V is thus a phasor representation of the sinusiod v(t)

So having show that you can see that a phasor is a complex number in a polar form.