Question

Find the cube roots of 27(cos 330° + i sin 330°).

Answer 1

Here's something.\[\left(\cos(x) + i\sin(x)\right)^n = \cos(nx) + i\sin(nx)\]Can give you the proof if you need.

Answer 2

hmm...

Answer 3

Oh, and the cube root is just an exponent. Guess which one...

Answer 4

lol, i dropped in a 3 instead of its upside down version

Answer 5

Ok I'm left with this 3√(27(√3/2-i/2))

Answer 6

\(\cos\left(\frac{1}{3} \cdot 330\right)\) (or cos(110)) and \(i\sin \left(\frac{1}{3} \cdot 330\right)\) (or sin(110)) seem to be complicated numbers, unless I am missing something.