Answer
$2 \sqrt 3 - 2 i$
Work Step by Step
The given complex number can be written in the rectangular form as follows: $r (\cos \theta +i \sin \theta) = a+i b$
Where, $a=r \cos \theta ; b =r \sin \theta $
Let us suppose that $z =4 (\cos (-30^{\circ}) +i \sin (-30^{\circ}) ) ....(1) $
We know that $\sin (-\theta) =- \sin \theta$ and $\cos (-\theta) =\cos \theta$
Therefore, the equation (1) becomes:
$4 (\cos (-30^{\circ}) +i \sin (-30^{\circ})) =4(\dfrac{\sqrt 3}{2} -i \dfrac{1}{2} ) \\ = 2 \sqrt 3 - 2 i$
