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        Complex	Analysis:	Problems	with	solutions
        Book	·	August	2016
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             Juan	Carlos	Ponce	Campuzano
             The	University	of	Queensland
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                ComplexAnalysis
                  Problems with solutions
                  JuanCarlosPonceCampuzano
            c
        Copyright 
 2016 Juan Carlos Ponce Campuzano
        PUBLISHED BY JUAN CARLOS PONCE CAMPUZANO
        This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike
        4.0 International License.
        License at: https://creativecommons.org/licenses/by-nc-sa/4.0/
        First e-book version, August 2015
                  Contents
                      Foreword .................................................... 5
                1     ComplexNumbers......................................... 7
                1.1   Basic algebraic and geometric properties                             7
                1.2   Modulus                                                             13
                1.3   Exponential and Polar Form, Complex roots                           16
                2     Functions ................................................... 21
                2.1   Basic notions                                                       21
                2.2   Limits, Continuity and Differentiation                              35
                2.3   Analytic functions                                                  39
                2.3.1 Harmonicfunctions ............................................ 45
                3     ComplexIntegrals ........................................ 49
                3.1   Contour integrals                                                   49
                3.2   CauchyIntegral Theorem and CauchyIntegral Formula                   55
                3.3   Improper integrals                                                  71
                4     Series ....................................................... 75
                4.1   Taylor and Laurent series                                           75
                4.2   Classification of singularities                                      85