A First Course in Complex Analysis · Problem 2.5.2

Differentiation — Beck, Marchesi, Pixton & Sabalka

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

Problem

Determine where the following functions are differentiable and compute their derivatives (or explain why they are not differentiable). ((a))

f(z) = iz + \operatorname{Re}(z)

((b))

f(z) = z|z|

((c))

f(z) = z^2 - \bar{z}

((d))

f(z) = |z|^2

((e))

f(z) = \dfrac{1}{z^3}