(i) | $f : \gamma([a, b]) \to \mathbb{C}$ is a D5635: Standard-continuous complex function |

**complex path integral**of $f$ with respect to $\gamma$ is the D1207: Complex number \begin{equation} \int_{\gamma} f(z) \, d z : = \int^b_a f(\gamma(t)) \gamma'(t) \, d t \end{equation}