Phasor representation
When multiplying complex numbers using the polar representation, we use the following formula:

$$(a\angle b)\times(c\angle d) = (a\times c)\angle(b+d)$$

That is, we multiply the radii, and add the angles.

This is a basic rule of polar representation. Polar form is just another way of representing Euler's formula:

$$r\angle \theta = r \mathrm{e}^{i \theta}=r\cos \theta+ir\sin \theta$$

So:

$$(a\angle b)\times(c\angle d) = (a \times \mathrm{e}^{i b}) \times (c\times  \mathrm{e}^{i d}) = a\times c\times \mathrm{e}^{i (b+d)} = (a\times c)\angle(b+d)$$



To build the formula, we can start in the other direction. We know for an inductor, that the reactance of an inductor is \$j\omega L\$ which when converted to polar representation becomes \$\omega L\angle 90^\circ\$.

We know the voltage across an inductor is:

$$\overline{V} = \overline{I}\times X_L$$

So then we can say:

$$\overline{V} = (\omega L\angle 90^\circ) \times (I∠\alpha^\circ)$$

$$= \omega L I\space\space\angle\space\space\alpha^\circ + 90^\circ$$