## Question

###### Consider P(z) = 2' + 2z-3 - i and, using the argument theorem and Rouche's theorem calculate the number of its roots in each of the following domains:(a) {:lz -1/ < 1;(b) (zIz - I/> 1lzl < 2} ,(c) {z/zl > 2/ .

Consider P(z) = 2' + 2z-3 - i and, using the argument theorem and Rouche's theorem calculate the number of its roots in each of the following domains: (a) {:lz -1/ < 1; (b) (zIz - I/> 1lzl < 2} , (c) {z/zl > 2/ .

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