Mathematics · Complex Analysis
Let P(z) be a non-constant polynomial over &complex;. For a given real number R > 0, let SR = {z ∈ &complex; : |P(z)| < R}. Which of the following statements is always true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1SR is an open subset of &complex;.✓
- 2SR is a bounded subset of &complex;.
- 3Every connected component of SR contains a zero of P(z).
- 4|P(z)| > R for every z on the boundary of SR.
Correct answer
SR is an open subset of &complex;.
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