Complex Analysis: Theory and Applications · Problem 4.1.13

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · sequence-limit-imaginary-part

Problem

Complete the proof of Theorem 4.1. In other words, suppose that

\displaystyle\lim_{n\to\infty} z_n = \zeta

, where

z_n = x_n + iy_n

and

\zeta = u + iv

. Prove that

\displaystyle\lim_{n\to\infty} y_n = v