functional equations - Show that for this function the stated is true.

For the function

$$G(w) = \frac{\sqrt2}{2}-\frac{\sqrt2}{2}e^{iw},$$
show that
$$G(w) = -\sqrt2ie^{iw/2} \sin(w/2).$$

Hey everyone, I'm very new to this kind of maths and would really appreciate any help. Hopefully I can get an idea from this and apply it to other similar questions. Thank you.