Complex Numbers Cubed
The complex number z can be cubed creating the complex number z^3 . We hypothesize that the geometric figure being transformed to z^3 will be rotated another π/2 radians because we are multiplying by another factor of i. We also expect the figure to dilate more since there is another factor of real numbers.
Line Segments
Here we can see that our predictions are true and that the parabolic shape on a closed interval becomes more dilated is rotated to π radians [2]. Seen in Figures 39 and 40. A horizontal preimage creates a parabolic shape that is vertical and is opened upward and the opposite follows when that line passes the real number axis. A vertical line segment creates a parabola on a closed interval that is horizontal and is opened towards the right and the opposite is created when it crosses the imaginary number axis.

Compared to the transformations of the line segments of z^2 the parabolas are rotated π/2 radians and it creates a more dilated curve. Mathematically this is logical because a function cubed will create a reflection across the line y = x and so that is why after crossing a certain axis the image flips. See Figures 41 and 42.

The same principles of rotating and dilating because of the multiplication of a complex number are applied to when the line segment is a positive slope and a negative slope. The image will be like the images of z^2 but it will be rotated another π/2 radians and the line segment will be more dilated. See Figures 43 and 44.
