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Title: Winding Number
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Series: Complex Analysis
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YouTube-Title: Complex Analysis 24 | Winding Number
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Bright video: https://youtu.be/FNvwQaKmQ2A
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Dark video: https://youtu.be/40wcBZZcI0w
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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: ca24_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 $\gamma: [a,b] \rightarrow \mathbb{C}$ be a curve where the image is the unit circle. What is correct for $z_0 = 5 + 5 i$?
A1: $ \mathrm{wind}(\gamma, z_0) = 0$
A2: $ \mathrm{wind}(\gamma, z_0) = 1$
A3: $ \mathrm{wind}(\gamma, z_0) = -1$
A4: $ \mathrm{wind}(\gamma, z_0) = 2$
Q2: Let $\gamma: [0,2] \rightarrow \mathbb{C}$ be given by $\gamma(t) = \exp(2\pi i t)$. Which statement is correct?
A1: $ \mathrm{wind}(\gamma, 0) = 2$
A2: $ \mathrm{wind}(\gamma, 2) = 1$
A3: $ \mathrm{wind}(\gamma, 0) = -1$
A4: $ \mathrm{wind}(\gamma, 1)$ is well-defined.
A5: $ \mathrm{wind}(\gamma, 2) = 2$
Q3: Let $\gamma: [0,1] \rightarrow \mathbb{C}$ given by $\gamma(t) = \exp(-2\pi i t)$. What is the winding number of $\gamma$ with respect to the origin?
A1: $-1$
A2: $0$
A3: $1$
A4: $2$
A5: $-2$
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Last update: 2024-10
