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Question 1: (a) Formulate maximum modulus principle for holomorphie functions and the Shwarz lemma. (b) Evaluate 1 f 1 + 22 d z c if

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(a) Formulate maximum modulus principle for holomorphie functions and the Shwarz lemma. (b) Evaluate 1 f 1 + 22 d z c if C is one of the circles |z+i|:1; |zi|:1; |z|:3. (a) Formulate Argument principle and Rouche theorem. (b) How many roots of the polynomial p(2) = 225 - 23 + 2+7 lie in the annulus 1

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