A First Course in Complex Analysis · Problem 2.5.3

Differentiation — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · limits-complex-functions

Problem

Prove that the limit of a complex function is unique: that is, if

\lim_{z \to z_0} f(z) = w_0

and

\lim_{z \to z_0} f(z) = w_1

, then

w_0 = w_1