Answer
$-1+\sqrt3i$
Work Step by Step
We know from the unit circle that:
$\cos 120^{\circ}=-\frac{1}{2}$
$\sin 120^{\circ}=\frac{\sqrt 3}{2}$
Thus,, we simplify the given expression as follows:
$2[\cos (120^{\circ})+i \ \sin (120^{\circ})]
\\=2 \left(-\dfrac{1}{2}+i\dfrac{\sqrt 3}{2}\right)
\\=2\left(-\frac{1}{2}\right)+2\left(i\cdot\frac{\sqrt3}{2}\right)\
\\=-1+\sqrt3i$
