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PDF-Homomorphisms1De nitionandexamplesRecallthat,ifGandHaregroups,anisomor PDF document

5ThecomplexexponentialDe nefCCbyfzez1Xn0zn nHereifzxiythenezexeiyexcosyisinyThefactthatfisahomomorphismfollowsfromtheidentityez1z2ez1ez2Thecomplexexponentialissurjectiveeve

5.(Thecomplexexponential.)De nef:C!Cbyf(z)=ez=1Xn=0zn n!:Here ifz=x+iy thenez=exeiy=ex(cosy+isiny):Thefactthatfisahomomorphismfollowsfromtheidentityez1+z2=ez1ez2:Thecomplexexponentialissurjective:eve

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Homomorphisms1De nitionandexamplesRecallthat,ifGandHaregroups,anisomor: Transcript

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