Answer
$ -\sqrt 3+i$
Work Step by Step
We know from the unit circle that:
$\cos \dfrac{5 \pi}{6}=\dfrac{- \sqrt 3}{2}$ and $\sin \dfrac{5 \pi}{6}=\dfrac{1}{2}$
Thus,, we simplify the given expression as follows:
$2\left[\cos (\dfrac{5\pi}{6})+i \ \sin (\dfrac{5 \pi}{6})\right]
\\=2\left(\dfrac{-\sqrt 3}{2} + i \dfrac{1}{2}\right)
\\=2\left(\dfrac{-\sqrt 3}{2}\right) + 2\left(i \dfrac{1}{2}\right)
\\= -\sqrt 3+i$
