A First Course in Complex Analysis · Problem 2.5.1

Differentiation — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · limits-continuity-complex-functions

Problem

Where are each of the following functions continuous? ((a))

f(z) = \dfrac{z^2 + 1}{z^2 - 1}

((b))

f(z) = \dfrac{1}{|z|^2 - 1}

((c))

f(x,y) = \dfrac{x + i(x+y)}{x^2 + y^2 - 1}

((d))

f(z) = \dfrac{z}{z + \bar{z}}