Using DeMoivre's Theorem, calculate ( sqrt(3) + i )^4.

I'm aware DeMoivre's Thm:
z^n=r^n (cos(ntheta)+isin(ntheta))

Question

Using DeMoivre's Theorem, calculate ( sqrt(3) + i )^4.

I'm aware DeMoivre's Thm: 
z^n=r^n (cos(ntheta)+isin(ntheta))

anonymous · Answer

i have r=2 that's it lol

anonymous · Answer

i have the triangle but not sure how to move on

kinggeorge · Answer

You don't have that much further to go. Since you have the triangle, you should have something like this.|dw:1375481685584:dw|All you need to do, is find the value of x, where x is that angle.

anonymous · Answer

i can't use a calculator

anonymous · Answer

got it

anonymous · Answer

cos(theta)=sqrt(3)/2

anonymous · Answer

theta=30 degrees

anonymous · Answer

is that correct?

kinggeorge · Answer

I believe that would be correct.

kinggeorge · Answer

Unless satellite disagrees? Have I been too hasty?

anonymous · Answer

thanks sorry i usually don't have so many questions too much stress for tomorrows Math CSET 112 :-(

anonymous · Answer

just to butt in for a second, since this is an adult problem, it really should be 
$$\theta =\frac{\pi}{6}$$ but i guess you can use 30

kinggeorge · Answer

Good point. You should usually have it as $\pi/6$ when using cosines and sines.