Question

Find (z)*2020/3 if z=cos11π/6 +isin7π/6.

Answer 1

We know that

$$\cos \dfrac{11\pi}{6}=\cos \dfrac{\pi}{6}=\dfrac{\sqrt{3}}{2}$$

$$\sin \dfrac{7\pi}{6}=-\sin \dfrac{\pi}{6}=-\dfrac12$$

So, then

$$z=\dfrac{\sqrt{3}}{2}-\dfrac12i$$

Finally,

$$z\cdot \dfrac{2020}{3}=\dfrac{1010\sqrt{3}}{3}-\dfrac{1010}{3}i.$$