A First Course in Complex Analysis · Problem 2.5.9

Differentiation — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · continuity-complex-functions

Problem

Define

g : \mathbb{C} \to \mathbb{C}

g(z) := \begin{cases} \dfrac{\bar{z}}{z} & \text{if } z \neq 0, \\ 1 & \text{if } z = 0. \end{cases}

Show that

g

is continuous at every

z \neq 0