Explore complex analysis in this comprehensive 41-minute video lecture covering essential topics from complex integration to the Residue theorem. Dive into an intuitive explanation of complex integration using Pólya vector field, and progress through key concepts such as Cauchy's theorem, integrating 1/z, and the Cauchy integral formula. Learn about the powerful Residue theorem and its applications, with real-world examples and insights. Gain a deeper understanding of complex analysis fundamentals, presented at a pace suitable for thorough comprehension, making it an ideal resource for students and enthusiasts alike.