The magnitude of this point is [tex]\sqrt{2^2+(-2\sqrt{3})^2} = \sqrt{16} = 4[/tex], so the magnitude is four.
We can finish the solution by trying the only two answers with magnitude four: A and B.
For option B, the rectangular coordinates are [tex](4 \cos \frac{4\pi}{3}, 4 \sin \frac{4\pi}{3}) = (-2, -2\sqrt{3})[/tex], so B is incorrect.
For option A, the rectangular coordinates are [tex](-4 \cos \frac{2\pi}{3}, -4 \sin \frac{2\pi}{3}) = (2, -2\sqrt{3})[/tex], so the answer is A.
