Mathematics · Complex Analysis
Let &Double_struck;× = {z ∈ &complex; : 0 < |z| < 1} be the punctured unit disk and let f be a bijective holomorphic map of &Double_struck;× onto itself. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There exists no θ ∈ ℝ such that f(z) = eiθz for all z ∈ &Double_struck;×.
- 2limz→0 f(z) = 0.✓
- 3limz→0 f(z) exists and has absolute value < 1.
- 4limz→0 f(z) does not exist.
Correct answer
limz→0 f(z) = 0.
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