This paper presents a novel cosmological model that applies the Cauchy residue theorem analogy through Gauss's divergence theorem to estimate the size of the observable universe. By treating supermassive black holes as gravitational residues at the cosmic center and incorporating dark matter distributions and dark energy effects within modified Friedmann equations, we derive a universe radius of 41.9 billion light-years. This result shows remarkable agreement (within 9.5%) with the ΛCDM-based observable universe radius of 46.3 billion light-years, demonstrating the viability of complex analysis techniques in cosmological scale calculations. 1