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Question Number 148960 by tabata last updated on 01/Aug/21
findtheresideof(z)=zzn−1
Answered by mathmax by abdo last updated on 02/Aug/21
lesresidusicisontlespolesdefetsesentlesracinesnemedelunitecadzk=ei2kπnandk∈[[0,n−1]]⇒f(z)=z∏k=0n−1(z−zk)f(z)=∑k=0∞akz−zk⇒Res(f,zk)=ak=zknzkn−1=zk2nautremethodef(z)=z(z−z0)....(z−zk−1)(z−zk)(z−zk+1)...(z−zn−1⇒Res(f,zk)=zk(zk−z0)...(zk−zk−1)(zk−zk+1)....(zk−zn−1)
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