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: $-2$