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Title: Identity Theorem
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Series: Complex Analysis
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YouTube-Title: Complex Analysis 30 | Identity Theorem
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Bright video: https://youtu.be/nFHEq7ljd0k
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Dark video: https://youtu.be/aAINMsQ8ZGY
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Ad-free video: Watch Vimeo video
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: ca30_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $f: \mathbb{C} \rightarrow \mathbb{C}$ be a holomorphic function with $f(\frac{1}{n}) = 0$ for all $n \in \mathbb{N}$. What is correct?
A1: Only the function $f(z) = 0$ satisfies the condition above.
A2: Only the two functions $f_1(z) = 0$ and $ f_2(z) = \sin \left( 2 \pi \frac{1}{z} \right) $ satisfy the conditions above.
A3: There are infinitely many functions that fulfil the conditions above.
A4: One needs more information.
Q2: Let $f: \mathbb{C}\setminus{0} \rightarrow \mathbb{C}$ be a holomorphic function with $f(\frac{1}{n}) = 0$ for all $n \in \mathbb{N}$. What is correct?
A1: Only the function $f(z) = 0$ satisfies the condition above.
A2: The two functions $f_1(z) = 0$ and $ f_2(z) = \sin \left( 2 \pi \frac{1}{z} \right) $ satisfy the conditions above.
A3: One needs more information.
Q3: Let $f: \mathbb{C} \rightarrow \mathbb{C}$ be a holomorphic function with $f(n) = 0$ for all $n \in \mathbb{N}$. What is correct?
A1: Only the function $f(z) = 0$ satisfies the condition above.
A2: The two functions $f_1(z) = 0$ and $ f_2(z) = \sin \left( 2 \pi z \right) $ satisfy the conditions above.
A3: One needs more information.
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Last update: 2024-10
