A First Course in Complex Analysis · Problem 2.5.15

Differentiation — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · cauchy-riemann-equations

Problem

Use the Cauchy--Riemann equations to show that the following functions are nowhere holomorphic: ((a))

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

((b))

f(z) = |z|

((c))

f(z) = |z|^2

((d))

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