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PDF-MATH106HOMEWORK5SOLUTIONS1.LetC1denotethepositivelyorientedcirclejzj=4 PDF document

3z21bfzz2 sinz 2cfzz 1ezSolutionWeneedtoshowthegivenfunctionsareholomorphicintheareabetweenandonthetwocurvescallitAForathezerosof3z21arei p 3theybothlieintheareaenclosedbyC1sothe

3z2+1(b)f(z)=z+2 sinz 2(c)f(z)=z 1ezSolution:Weneedtoshowthegivenfunctionsareholomorphicintheareabetweenandonthetwocurves callitAFor(a) thezerosof3z2+1arei p 3 theybothlieintheareaenclosedbyC1 sothe

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