第一章-复数与复变函数

这可让他犯了难，施工现场距离项目部很远，没有车还真是不方便office,branchoffices(jurisdiction),riskmanagement,marketingmanagementsectorthroughsupervisionandinspectionfoundproblems,shouldbeassignedtheinvestigatorsarecorrectedinatimelymanner.27ththefifthchapterpenaltyunderanyofthefollowingacts,thentherelevantprovisionstopunishtheinvestigators,accordingtotheBank.Toconstituteacrimeshallbeinvestigatedforcriminalresponsibility:(A)onthebusinessthatarenotinvolvedintheinvestigation,issuedasurvey.(B)customercreditinformationarenotthoroughverification.(Iii)toparticipateincreditcustomersurveyisnotinplace,customersanddataisincomplete,untrue;heknowsbearacounterfeitedclientsissuingcredit.(D)doesnotprovideforduediligenceofcreditbusiness,pre-loaninvestigationform,concealingfactsorprovidingfalseinformationorshouldbefoundinanormalinvestigationfailedtodiscovertheriskfactors,leadtothereviewandapprovalpolicyerrors,loanrisk.(Five)onloanguaranteesofsurveynotinplace,notbyprovidesonarrived,andpledgerealforfieldverification,andassessment,andidentificationandregistration,notaccordingtoprovidesonguarantorofguaranteesqualificationandguaranteescapacityforsurveyverified,ledtoguaranteesloanlostauthenticity,andlegitimacy,andeffectivenessof;cycleloanbusinessintheofmortgage引言复数理论的产生、发展经历了漫长而又艰难的岁月．复数是16世纪人们在解代数方程时引入的．1545年，意大利数学物理学家HCardan（卡丹）在所著《重要的艺术》一书中列出将10分成两部分，使其积为40的问题，即求方程(10)xx的根，它求出形式的根为515和515，积为25(15)40．但由于这只是单纯从形式上推广而来引进，并且人民原先就已断言负数开平方是没有意义的．因而复数在历史上长期不能为人民所接受．“虚数”这一名词就恰好反映了这一点．直到十八世纪，,DAlembert（达朗贝尔）：LEuler（欧拉）等人逐步阐明了复数的几何意义与物理意义，建立了系统的复数理论，从而使人民终于接受并理解了复数．复变函数的理论基础是在十九世纪奠定的，主要是围绕..ALCauchy（柯西），KWeierstrass（魏尔斯特拉斯）和BRiemann（黎曼）三人的工作进行的．到本世纪，复变函数论是数学的重要分支之一，随着它的领域的不断扩大而发展成庞大的一门学科，在自然科学其它（如空气动力学、流体力学、电学、热学、理论物理等）及数学的其它分支（如微分方程、积分方程、概率论、数论等）中，复变函数论都有着重要应用．这可让他犯了难，施工现场距离项目部很远，没有车还真是不方便office,branchoffices(jurisdiction),riskmanagement,marketingmanagementsectorthroughsupervisionandinspectionfoundproblems,shouldbeassignedtheinvestigatorsarecorrectedinatimelymanner.27ththefifthchapterpenaltyunderanyofthefollowingacts,thentherelevantprovisionstopunishtheinvestigators,accordingtotheBank.Toconstituteacrimeshallbeinvestigatedforcriminalresponsibility:(A)onthebusinessthatarenotinvolvedintheinvestigation,issuedasurvey.(B)customercreditinformationarenotthoroughverification.(Iii)toparticipateincreditcustomersurveyisnotinplace,customersanddataisincomplete,untrue;heknowsbearacounterfeitedclientsissuingcredit.(D)doesnotprovideforduediligenceofcreditbusiness,pre-loaninvestigationform,concealingfactsorprovidingfalseinformationorshouldbefoundinanormalinvestigationfailedtodiscovertheriskfactors,leadtothereviewandapprovalpolicyerrors,loanrisk.(Five)onloanguaranteesofsurveynotinplace,notbyprovidesonarrived,andpledgerealforfieldverification,andassessment,andidentificationandregistration,notaccordingtoprovidesonguarantorofguaranteesqualificationandguaranteescapacityforsurveyverified,ledtoguaranteesloanlostauthenticity,andlegitimacy,andeffectivenessof;cycleloanbusinessintheofmortgage第一章复数与复变函数§1复数与复数运算教学目的与要求：了解复数的概念及复数的模与辐角；掌握复数的代数运算复数的乘积与商﹑幂与根运算.教学重点：德摩弗()DeMoiVre公式.教学难点：德摩弗()DeMoiVre公式.教学方法：课时：2学时.1．复数域形如zxiy或zzyi的数，称为复数，其中x和y均是实数，称为复数z的实部和虚部，记为Rexz，Imyz1i，称为虚单位．两个复数111zxiy，与222zxiy相等，当且仅当它们的实部和虚部分别对应相等，即12xx且12yy虚部为零的复数可看作实数，即0xix，特别地，000i，因此，全体实数是全体复数的一部分．实数为零但虚部不为零的复数称为纯虚数，复数xiy和xiy称为互为共轭复数，记为()xiyxiy或xiyxiy设复数111zxiy，222zxiy，则复数四则运算规定：121212()()zzxxiyy1212121221()()zzxxyyixyxy1121221122222222222(0)zxxyyxyxyizzxyxy容易验证复数的四则运算满足与实数的四则运算相应的运算规律．全体复数并引进上述运算后称为复数域，必须特别提出的是，在复数域中，复数是不能比较大小的．２．复平面从上述复数的定义中可以看出，一个复数zxiy实际上是由一对有序实数(,)xy唯一确定．因此，如果我们把平面上的点(,)xy与复数zxiy对应，就建立了平面上全部的点和全体复数间的一一对应关系．由于x轴上的点和y轴上非原点的点分别对应着实数和纯虚数，因而通常称x轴为实轴，称y轴为虚轴，这样表示复数z的平面称为复平面或z平面．引进复平面后，我们在“数”与“点”之间建立了一一对应关系，为了方便起见，今后这可让他犯了难，施工现场距离项目部很远，没有车还真是不方便office,branchoffices(jurisdiction),riskmanagement,marketingmanagementsectorthroughsupervisionandinspectionfoundproblems,shouldbeassignedtheinvestigatorsarecorrectedinatimelymanner.27ththefifthchapterpenaltyunderanyofthefollowingacts,thentherelevantprovisionstopunishtheinvestigators,accordingtotheBank.Toconstituteacrimeshallbeinvestigatedforcriminalresponsibility:(A)onthebusinessthatarenotinvolvedintheinvestigation,issuedasurvey.(B)customercreditinformationarenotthoroughverification.(Iii)toparticipateincreditcustomersurveyisnotinplace,customersanddataisincomplete,untrue;heknowsbearacounterfeitedclientsissuingcredit.(D)doesnotprovideforduediligenceofcreditbusiness,pre-loaninvestigationform,concealingfactsorprovidingfalseinformationorshouldbefoundinanormalinvestigationfailedtodiscovertheriskfactors,leadtothereviewandapprovalpolicyerrors,loanrisk.(Five)onloanguaranteesofsurveynotinplace,notbyprovidesonarrived,andpledgerealforfieldverification,andassessment,andidentificationandregistration,notaccordingtoprovidesonguarantorofguaranteesqualificationandguaranteescapacityforsurveyverified,ledtoguaranteesloanlostauthenticity,andlegitimacy,andeffectivenessof;cycleloanbusinessintheofmortgage我们就不再区分“数”和“点”及“数集”和“点集”．3．复数的模与幅