(a) Find the limit $\lim_{z \to 0} \frac{\text{Re } z + \text{Im } z}…

Question

(a) Find the limit $\lim_{z \to 0} \frac{\text{Re } z + \text{Im } z}{|z|^2}$.

(b) Prove that $f(z) = \cosh z$ is an entire function and find its derivative.

(c) Find the bilinear transformation that maps from \{1, i, -1\} to \{i, 0, -1\}.