Explore the fundamental concepts of complex analysis in this 50-minute lecture from the Engineering Mathematics course at the University of Washington. Delve into roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions. Learn about the Lorentz dilation factor, tachyons, inverse functions, and roots of positive one. Examine weird functions and their properties. Access accompanying lecture notes and the course website for additional resources and in-depth study materials.