Which expression is a cube root of -2i?1) 3sqrt2(cos(210))+isin(210))2) 3sqrt2(cos(260))+isin(260))3) 3sqrt2(cos(90))+isin(90))4) 3sqrt2(cos(60))+isin(60))

To use De Moivre's theorem, we first write -2i is cis form: 0 - 2i has r = 2 and theta = 270.
Then we take the cube root, which means the new result will have r^(1/3), and the angle (theta/3). This means r = cbrt(2) and theta = 90.
This means that the answer is (cube root of 2)(cos90 + i*sin90), choice C.

I suspect the choices "3sqrt2" is actually a cube root of 2, not 3 multiplied by the square root of 2.