complex-functions- examples concerning complex numbers.pdf

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1、Complex Functions c1 Examples concerning Complex Numbers Leif Mejlbro Download free books at LeifMejlbroComplexFunctionsc-1ExamplesconcerningComplexNumbersComplexFunctionsc-1–ExamplesconcerningComplexNumbers©2008LeifMejlbro&VentusPublishingApSISBN978-87-7681-385-7ComplexFun

2、ktionsc-1ContentsContentsIntroduction51.Thecomplexnumbers62.Polarformofcomplexnumbers313.Thebinomialequation394.Equationsofseconddegree545.Rationalandmultiplerootsinpolynomials626.Symboliccurrentsandvoltages727.Geometricalpointsets73Fast-trackyourcareerMastersinManagementSt

3、andoutfromthecrowdDesignedforgraduateswithlessthanoneyearoffull-timepostgraduateworkexperience,LondonBusinessSchool’sMastersinManagementwillexpandyourPleaseclicktheadvertthinkingandprovideyouwiththefoundationsforasuccessfulcareerinbusiness.Theprogrammeisdevelopedinconsultat

4、ionwithrecruiterstoprovideyouwiththekeyskillsthattopemployersdemand.Through11monthsoffull-timestudy,youwillgainthebusinessknowledgeandcapabilitiestoincreaseyourcareerchoicesandstandoutfromthecrowd.LondonBusinessSchoolApplicationsarenowopenforentryinSeptember2011.Regent’sPar

5、kLondonNW14SAUnitedKingdomFormoreinformationvisitwww.london.edu/mim/Tel+44(0)2070007573Emailmim@london.eduemailmim@london.eduorcall+44(0)2070007573www.london.edu/mim/4ComplexFunktionsc-1IntroductionIntroductionThisisthefirstbookcontainingexamplesfromtheTheoryofComplexFunctio

6、ns.Allthefollowingbookswillhavethisbookastheirbackground.EvenifIhavetriedtobecarefulaboutthistext,itisimpossibletoavoiderrors,inparticularinthefirstedition.Itismyhopethatthereaderwillshowsomeunderstandingofmysituation.LeifMejlbro27thMay20085ComplexFunktionsc-1Thecomplexnumbe

7、rs1ThecomplexnumbersExample1.1Splitacomplexfractionintoitsrealandimaginarypart.Leta+ib=0andc+idbetwocomplexnumbers,wherea,b,c,d∈R.Sinceingeneral,z·z=(x+iy)(x−iy)=x2+y2=

8、z

9、2,wegetbyamultiplicationwiththecomplexconjugatedofthedenominatorinboththenumeratorandthedenominatortha

10、tc+idc+ida−ibac+bdad−bc=·=+i·,a+iba+iba−iba2+b2a2+b2andweimmediatelysplitintothere