Find the exact value of $\cos \frac{11\pi}{12}$ and $\sin \frac{11\pi}{12}$ Find the exact values of those two numbers but by using the two following complex numbers complexs numbers : 
$$z = \frac{-\frac{\sqrt3}{2} -i\frac{1}{2}}{\sqrt8}$$
and 
$$w = \frac{\frac{\sqrt2}{2} +i\frac{\sqrt2}{2}}{\sqrt8}$$
I added them up and computed $z/w$ but it led me to nowhere I feel like I have to do some combined computation with those rwo complex numbers and then by identification I can know the exact values but I haven't found the right operations to do yet.
help me please.

$$\cos\frac{\pi}{12}+i\sin\frac{\pi}{12} = e^{i\pi/12} = e^{i\pi/3}\cdot e^{-i\pi/4} \tag{1}$$
$$ = \left(\frac{1}{2}+i\frac{\sqrt{3}}{2}\right)\cdot\left(\frac{\sqrt{2}}{2}-i\frac{\sqrt{2}}{2}\right) \tag{2}$$
$$ = \left(\frac{\sqrt{2}}{4}+\frac{\sqrt{6}}{4}\right)+i\left(\frac{\sqrt{6}}{4}-\frac{\sqrt{2}}{4}\right)\tag{3} $$
hence
$$ \cos\frac{11\pi}{12} = -\frac{\sqrt{2}+\sqrt{6}}{4},\qquad \sin\frac{11\pi}{12}=\frac{\sqrt{6}-\sqrt{2}}{4}.\tag{4}$$
