Evaluate (1+sqrt(3)i)^12 using DeMoivre's theorem. plz show all work
Converting to polar form, we get 1 + sqrt(3)*i = sqrt(2)(cos 60 + i sin 60).
Then (1 + sqrt(3)*i)^12 = sqrt(2)^12 (cos 60 + i sin 60)^12
= 64 (cos 720 + i sin 720)
= 64
The answer is 64.
Like so:
