Question

Which expression is a cube root of 2?
A) Cube root of 2 (cos (120 degrees) + i sin (120 degrees))
B) Cube root of 2 (cos (40 degrees) + i sin (40 degrees))
C) Cube root of 2 (cos (280 degrees) + i sin (280 degrees))

Answer 1

using eulers formula e^ix = cosx+isinx

Answer 2

bad picture, but it is supposed to represent the complex plane. the real cube root of 2 is on the real axis. divide the circle up into 3 equal parts to find the other one. since you are dividing the circle up into 3 parts, each part is 360/3=120 degrees

Answer 3

so there are two answers, but only one of your choices works it is
\[\sqrt[3]{2}(\cos(120)+i\sin(120))\] and
\[\sqrt[3]{2}(\cos(240)+i\sin(240))\]