Answer
($-2+i2\sqrt 3$)
Work Step by Step
Given Complex number is 4($\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}$) .........(1)
$\frac{2\pi}{3} = 2\times\frac{180}{3}$
$\frac{2\pi}{3} = 120$
we know that
$\cos 120^{\circ}= \frac{-1}{2}$ and $\sin 120^{\circ}= \frac{\sqrt 3}{2}$
Substitute these values in equation (1) we get
4($\frac{-1}{2}+i\frac{\sqrt 3}{2}$) = ($\frac{-4}{2}+i\frac{4\sqrt 3}{2}$)
=($-2+i2\sqrt 3$)
Hence the standard form is ($-2+i2\sqrt 3$)
