10.1.30 Integral of a complex variable

Problem: Calculate the integral along the curve \( \mathcal{L} \). \[ \begin{array}{l} \int_{\mathcal{L}} z \operatorname{Re} z^{2} d z, \\ \mathcal{L}=\widetilde{A B}=\left\{z:|z|=2, \quad \operatorname{Im} z \geq 0, \quad z_{A}=2, \quad z_{B}=-2 .\right. \end{array} \]