i) Find all solutions to the equation z³ = 8i. Make sure to give your answers in Cartesian coordinates.

(ii) Consider the map f : C C defined by f(z) = z³ . Express this map in polar coordinates. This means if z = {r, } are the polar coordinates of a point z C, what are the polar coordinates of the image f(z) = {r' , '}?

(iii) Visualize the map from (ii) by drawing how the rays R() = {z C : arg(z) = } for = 0, /4, /2, 3/4, , 5/4, 3/2, 7/4, as well as the circles S(0, 1), S(0, 1/2) are mapped. Clearly label your picture.