The images below show Julia sets and basins of attraction related to the function $f(z)=z^5-1$. I emphasize *related to*; the basins of attraction of $f$ are not shown.

The first image shows the basins of attraction of $N(z)$, where $N$ is the Newton's method function for $f$.**Problem 1**: Write down the function $N$ whose Julia set is shown in figure 1.

The second and third images are obtained by conjugating $N$ so that zero maps to $-1$ and $\infty$ maps to 1.**Problem 2**: Indicate a strategy to find the funciton that generated those figures.