Q1: Let $\gamma: [0,1] \rightarrow \mathbb{C}$ be piecewise continuously differentiable. What is not correct?

A1: $\gamma$ is continuous.

A2: There are $a_i \in [0,1]$ such that $\gamma|{[a_i,a{i+1}]}$ is continuous.

A3: There are $a_i \in [0,1]$ such that $\gamma|{[a_i,a{i+1}]}$ is differentiable.

A4: There are $a_i \in [0,1]$ such that $\gamma|{[a_i,a{i+1}]}$ is continuously differentiable.

A5: There are $a_i \in [0,1]$ such that $\gamma|{[a_i,a{i+1}]}$ is two-times differentiable.

Q2: Let $\gamma: [0,2 \pi] \rightarrow \mathbb{C}$ be given by $\gamma(t) = e^{it}$ and $f(z) = \frac{1}{z}$. What is $ \oint_\gamma f(z) , dz $?

A1: $0$

A2: $1$

A3: $2 \pi i$

A4: $i$

Q3: Let $\gamma: [a,b] \rightarrow \mathbb{C}$ be a piecewise continuously differentiable. What do we need to say that $\gamma$ is closed?

A1: $\gamma(a) = 0$

A2: $\gamma(a) = \gamma(b)$

A3: $\gamma(a) = \gamma(b) = 0$

A4: $\gamma(a) = 1$

Q4: Let $\gamma: [a,b] \rightarrow \mathbb{C}$ be a piecewise continuously differentiable and $\gamma^-$ the curve with reversed orientation. What is correct?

A1: $ \int_\gamma f(z) , dz = 0$

A2: $ \int_\gamma f(z) , dz = \int_{\gamma^-} f(z) , dz$

A3: $ \int_\gamma f(z) , dz = -\int_{\gamma^-} f(z) , dz$

A4: $ \int_\gamma f(z) , dz = 2 \int_{\gamma^-} f(z) , dz$