A Crash Course on Complex Derivatives and e^x

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by Super User, 4 years ago
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In my video explaining Euler's formula, I gave the intuition for why the function e^x takes the imaginary line in the complex plane, and wraps it around a circle with radius 1, preserving lengths. However, I had to appeal to the vague fact that e^x is "natural". This video introduces the notion of a complex derivative, and how the fact that e^x is its own derivative explains why it acts in the "natural" way we might expect.

Music: "Sundays" by Time For Three, http://www.tf3.com/