Mathematics · Complex Analysis
Let D = {z ∈ ℂ : |z| < 1}. Consider the following statements: (a) Let f : D → D be a holomorphic function. Suppose α, β are distinct complex numbers in D such that f(α) = α and f(β) = β. Then f(z) = z for all z ∈ D. (b) There does not exist a bijective holomorphic function from D to the set of all complex numbers whose imaginary part is positive. (c) Let f : D → D be a holomorphic function. Suppose α ∈ D is such that f(α) = α and f'(α) = 1. Then f(z) = z for all z ∈ D. Which of the following options is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Both (a) and (c) are true.✓
- 2Both (a) and (b) are false.
- 3(a) is true and (c) is false.
- 4(a), (b) and (c) are all true.
Correct answer
Both (a) and (c) are true.
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