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Consider iteration of the function \(f(z)=z^3\text{.}\)

- Show that zero is a super-attractive fixed point of \(f\text{.}\)
- Show that the orbit of \(z_0\) tends to zero whenever \(|z_0| \lt 1\) but diverges to \(\infty\)
- Explain precisely why \(f\) displays sensitive dependence on initial conditions.
- Compute the orbits of \(e^{\pi i/3}\) and \(e^{\pi i/4}\text{.}\)