What Do Complex Functions Look Like - Essence of Complex Analysis

Explore the visual representations of complex functions in this comprehensive video tutorial. Dive into plots and animations of various complex operations, including addition and multiplication of constants, exponentiation, power functions (with integer powers and roots), and logarithms. Examine concepts like branch cuts, branch points, and Riemann surfaces. Witness a unique 4D rotation of Riemann surfaces and their inverse functions. Pause to absorb the detailed visuals or simply appreciate the intricate plots and animations. Discover interesting vector plots for power functions, including multipole expansions relevant to electromagnetism. Gain insights into the visualization methods for complex functions and prepare for future discussions on the Problem of Apollonius.

Introduction.
Adding constant.
Multiplying constant.
Exponentiation.
Power function - integer powers.
Power function - complex inversion.
Power function - square root branches.
Power function - Riemann surfaces.
Logarithm.
Logarithm - 4D rotation.