e) The cube roots of 1 are plotted on the diagram below. Im(z) /3 e-2i/3 1...

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e) The cube roots of 1 are plotted on the diagram below. Im(z) /3 e-2i/3 1 Re(z) i) Show that if w is a cube root of 1 then -2iw is a cube root of 8i. ii) Hence, by rotating and scaling the diagram above, plot and label the cube roots of 8i. Indicate the angle of rotation and scaling factor. iii) Find, in Cartesian form, z such that (z+1) 3 = 8i and Re(2) > 0. e) The cube roots of 1 are plotted on the diagram below. Im(z) /3 e-2i/3 1 Re(z) i) Show that if w is a cube root of 1 then -2iw is a cube root of 8i. ii) Hence, by rotating and scaling the diagram above, plot and label the cube roots of 8i. Indicate the angle of rotation and scaling factor. iii) Find, in Cartesian form, z such that (z+1) 3 = 8i and Re(2) > 0.