Anyone able to explain DeMovire's Theorem? If someone could walk me through this problem it would be greatly appreciated:

Find all fourth roots of $$8(1 + \sqrt{3}i)$$; that is, find all complex numbers z such that

$$z^{4} = 8(1 + \sqrt{3}i)$$

Polar coordinate
$$r = \sqrt{1^2 + (\sqrt3)^2} = 2$$

$$\theta = \arcsin(\frac{1}{2}) = \frac{\pi}{3}$$

thus we have,

$$z=8(2e^{\frac{\pi}{3}i})$$

The final answer is,

z_0 = 2e^pi(i)/12
z_1 =2e^(7pi)i/12
z_2 = 2e^(13pi)i/12
z_3 = 2e^(19pi)i/12

Question

Anyone able to explain DeMovire's Theorem? If someone could walk me through this problem it would be greatly appreciated:

Find all fourth roots of $$8(1 + \sqrt{3}i)$$; that is, find all complex numbers z such that 

$$z^{4} = 8(1 + \sqrt{3}i)$$

Polar coordinate
$$r = \sqrt{1^2 + (\sqrt3)^2} = 2$$

$$\theta = \arcsin(\frac{1}{2}) = \frac{\pi}{3}$$

thus we have,

$$z=8(2e^{\frac{\pi}{3}i})$$

The final answer is,

z_0 = 2e^pi(i)/12
z_1 =2e^(7pi)i/12
z_2 = 2e^(13pi)i/12 
z_3 = 2e^(19pi)i/12