Please help! I give medals and become a fan!
use de moivre's theorem to write the complex number in standard form.
(sqrt2(cos(15)+i sin(15))^6

Question

Please help! I give medals and become a fan!
use de moivre's theorem to write the complex number in standard form. 
(sqrt2(cos(15)+i sin(15))^6

anonymous · Answer

a. 4-4sqrt3 i
b. -8
c. 8i
d. -4sqrt3 +4i

psymon · Answer

Well, when you want to find some power of a complex number in polar form:
$$r(\cos \theta + isin \theta)^{n}$$, we need to follow this formula:
$$r ^{n}(\cos(n \theta) + isin(n \theta))$$ SO basically, your power is 6. SO that means we must do:
$$\sqrt{2}^{6}(\cos(6*15) + isin(6*15))$$
Think you can get that for me and then we'll finish?

anonymous · Answer

8(cos(90)+isin(90))

anonymous · Answer

@Psymon what is the next step? :)

psymon · Answer

I apologize, doing too much work, haha. Okay, awesome. So now what is the cos(90) and sin(90)?