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.
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This video was produced at the University of Washington
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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