Answer
$-4+i4\sqrt 3$
Work Step by Step
Given complex number is 8($\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}$)....(1)
$\frac{2\pi}{3}$ = $\frac{2\times 180}{3}$
= 120
We know that
$\cos120^{\circ} = \frac{-1}{2}$ and $\\sin120^{\circ} = \frac{\sqrt 3}{2}$
plugin these values in equation (1) we get
8($\frac{-1}{2}+i\frac{\sqrt 3}{2}$) = 4(-1+i$\sqrt 3$)
= $-4+i4\sqrt 3$
Hence the standard form is $-4+i4\sqrt 3$
