10.1.50 Integral of a complex variable
condition: Calculate the integral of a complex variable. \[ \oint_{|z+3 i|=2}\left(\frac{4}{(z-1+3 i)^{2}(z-3+3 i)}\right) d z \]
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.