10.1.47 Integral of a complex variable
Condition: Calculate the integral of a complex variable: \[ \int_{L}\left(z^{2}+z \cdot \bar{z}\right) d z, \quad L-\text { domain boundary } \] \[ D=\left\{z:|z-1|<1.0<\arg z<\frac{\pi}{2}\right\} \]
Calculation of integrals from functions of a complex variable. Sub-integral functions can be either analytic or with singular points. Application of the main residue theorem, as well as the Cauchy formulas for calculating integrals of functions with poles in a simply connected domain.