You can simplify this as -2(1+sqrt(3)i). This is not needed, but I like to work with easier terms. Next, you remember that z=r(cos(theta)+isin(theta)). r is called the modulus of z and it is defined as sqrt(x^2+y^2)=|z|. Yes, that's the same symbol for the absolute value, but in complex numbers, it defines the modulus. (This has to do with metric spaces)
Hence, r=2
Now, to find theta which is also called the argument of z, you use tan^-1(sqrt(3)/1)=pi/3
The proof of this lies in basic trigonometry, but it is more easily seen from Euler's Formula and unit vectors.
Now, not forgetting the -2 at the beginning, we get:
-2(1+sqrt(3)i)=-4(cos(pi/3)+isin(pi/3))
