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3) Answer the following questions considering the complex functions given below. a) Using the definition of complex derivative, evaluate f'(z) expression using derivative operation based on limiting case as lim . Az-0 a.1. f(z) = (z # 0). a.2. f(z) = (z # -1). z+1 b) For the following complex functions, determine where they are analytic or not, and state that where their derivative exists. Then, find the derivatives of these functions. b.1. f(z) = |z|² – 2z b.2. f(z) = x + icos(y) where z = x+ iy.

3) Answer the following questions considering the complex functions given below. a) Using the definition of complex derivative, evaluate f'(z) expression using derivative operation based on limiting case as lim . Az-0 a.1. f(z) = (z # 0). a.2. f(z) = (z # -1). z+1 b) For the following complex functions, determine where they are analytic or not, and state that where their derivative exists. Then, find the derivatives of these functions. b.1. f(z) = |z|² – 2z b.2. f(z) = x + icos(y) where z = x+ iy.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3) Answer the following questions considering the complex functions given below. a) Using the definition of complex derivative, evaluate f'(z) expression using derivative operation based on limiting case as lim . Az-0 a.1. f(z) = (z # 0). a.2. f(z) = (z # -1). z+1 b) For the following complex functions, determine where they are analytic or not, and state that where their derivative exists. Then, find the derivatives of these functions. b.1. f(z) = |z|² – 2z b.2. f(z) = x + icos(y) where z = x+ iy.
Transcribed Image Text:3) Answer the following questions considering the complex functions given below. a) Using the definition of complex derivative, evaluate f'(z) expression using derivative operation based on limiting case as lim . Az-0 a.1. f(z) = (z # 0). a.2. f(z) = (z # -1). z+1 b) For the following complex functions, determine where they are analytic or not, and state that where their derivative exists. Then, find the derivatives of these functions. b.1. f(z) = |z|² – 2z b.2. f(z) = x + icos(y) where z = x+ iy.
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