Rotating a vector 90° then pushing it through f must match pushing first then rotating – otherwise the map isn’t complex-differentiable. These grids make that concrete: the top shows df(zX) while the bottom shows z·df(X); forcing them equal unpacks straight into the Cauchy-Riemann pair ∂u/∂x = ∂v/∂y ∂u/∂y = −∂v/∂x. Aircraft engineers lean on exactly these relations when they build conformal maps to forecast airflow over wing sections, skipping full Navier-Stokes runs for early design loops. Which single arrow in the picture finally made the two equations feel inevitable to you?

Nieves María Josefa Vázquez Peteira is one of the oldest active drivers in Spain. At 102, she lives in Santalla de Rioaveso, located in the Galician municipality of Cospeito (Lugo). She obtained her driver's license out of pure necessity in the 1990s at the age of 69. Since then, she has been driving her trusted Citroën ZX almost daily.