1. If is analytic in a closed bounded region and in , show that assumes its minimum value on the boundary of . Hint: consider . 2. Use Problem 1 to prove the Fundamental Theorem of Algebra.
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Originally Posted by chiph588@ 1. If is analytic in a closed bounded region and in , show that assumes its minimum value on the boundary of . Hint: consider . The minimum value of is the maximum value of . But assumes it maximum on the boundary by the maximum modulos principle.
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