Complex Analysis L01: Overview & Motivation, Complex Arithmetic, Euler's Formula & Polar Coordinates

This is the first overview lecture in a new short-course on complex analysis. Here we motivate and introduce complex numbers z=x+iy, discuss how they are solutions to differential equations, and explain how to perform basic arithmetic, such as addition, subtraction, multiplication, and division. We also introduce Euler's formula and complex numbers in polar coordinates. @eigensteve on Twitter eigensteve.com databookuw.com This video was produced at the University of Washington %%% CHAPTERS %%% 0:00 Introduction and motivation 10:00 Euler's formula 11:27 Complex addition, subtraction, multiplication, and division 17:33 Complex numbers in polar coordinates: Radius and phase angle 26:16 Where this is going