Complex Analysis - Analytic Functions

Please answer the attached complex analysis questions. i.e. Prove the following generalization of proposition ... if g is analytic, if f is analytic

Verify the statement

Problem 10 ONLY 10) Verify the statement made in the text that if f is continuous at the point z, then... (see attachment)

Consider the shaded doman D

Problem 14 ONLY 14) Consider the shaded doman D in the attached figure bounded by the simple closed... (see attachment)

Comlpex 4.3.6 with theorem.

please latex solutions or use a math symbol editor

Prove that │∑ zn │ ≤ ∑│zn │ where zn is a complex number.

Functions of a Complex Variables ∞ ∞ Prove that │∑ zn │ ≤ ∑│zn │ where zn is a complex number. n =1 n =1