Part c
Discuss the conditions under which the iteration \(z_{n+1}=z_n^2+c\) converges. Explain how analyzing the magnitude of \(z_n\) and using the polar form in conjunction with De Moivre’s Theorem can assist in determining the convergence of such iterative mappings. Specifically, consider the role of \(|z_n|\) and the argument of \(z_n\) in convergence analysis.