Lo Strano fenomeno dell'AMPLITWIST Complesso: La genesi della derivata complessa f'(z)

⭐️Subscribe and get on the science spaceship ⭐️:    / @yousciences   In this video we discover the geometric heart of complex analysis: the concept of amplitwist. Starting from simple transformations like z^2, we see how each holomorphic function acts locally as an operation that stretches and rotates infinitesimal vectors — without ever distorting the angles. Through visual examples and progressive zooms, we explore how the complex derivative is much more than a number: it is a lens that shows the local structure of the function as a direct similarity. We also delve into the connection between differentiability, local linearity and the surprising property of conformity, namely the conservation of angles. A clear and intuitive journey into the heart of complex analysis, where calculus meets geometry. #amplitwist #complexanalysis #complexderivative #conformity #holomorphicfunctions #complexgeometry #visualmathematics #mathematicalzoom #jacobian #differentiability #similarities #complextransformations #conformalfunctions #tangentvectors #1shapes #realanalysis #linearapproximation #differentialcalculus #mathematicalintuition #creativemathematics #yousciences #doctorgiux #giux ⭐️Subscribe and get on the science spaceship ⭐️:    / @yousciences   💖Our Subscribers💖: https://www.yousciences.it/membership/ Where to find me 💎: ➤YOUSCIENCES: https://www.yousciences.it/ ➤OFFICIAL WEBSITE: https://www.giuseppesottile.it/ ➤INSTAGRAM: @yousciences @___giux___ ➤FACEBOOK:   / giuseppe.sottile.56   ➤LINKEDIN:   / giuseppe-sottile-3a8599b0   ➤TELEGRAM: https://t.me/joinchat/abNZYJqE7MVlODA0 ➤TIKTOK: https://www.tiktok.com/@yousciences?l... Other videos of: Analysis Complex⚛️:    • Analisi Complessa   📽️ VIDEO STREAM ALL: https://www.yousciences.it/videostream/ https://www.giuseppesottile.it/video.php 06:40 Err: corrects the drawing on the right "must be rotated by 2theta" Chapter Summary 00:00 Ouverture 02:24 How do I derive a complex function? 03:31 A Bizarre Phenomenon 04:00 Amplitwist 04:31 Example: Complex Power Function 09:13 Decomposition in the Fields (x,y) and (u,v) 14:10 Conformal Effect 15:40 Jacobian 20:00 Jacobian of z^2 21:00 The Derivative as an Amplitwist Executive Production by GIUX