Chapter 4.5, Problem 73E

(a)

To determine

Whether the complex number $\frac{1}{2}\left(\cos 0°+i\sin 0°\right)$ is in the prisoner set or the escape set of the function $f\left(z\right)=z^2-1$.

(b)

To determine

Whether the complex number $\sqrt{2}\left(\cos 30°+i\sin 30°\right)$ is in the prisoner set or the escape set of the function $f\left(z\right)=z^2-1$.

(c)

To determine

Whether the complex number $\sqrt[4]{2}\left(\cos \frac{\pi }{8}+i\sin \frac{\pi }{8}\right)$ is in the prisoner set or the escape set of the function $f\left(z\right)=z^2-1$.

(d)

To determine

Whether the complex number $\sqrt{2}\left(\cos \pi +i\sin \pi \right)$ is in the prisoner set or the escape set of the function $f\left(z\right)=z^2-1$.