Uploaded August 2019 | Updated September 2026, 3 weeks ago

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I'm finally back from my self-imposed exile, and there's no better way to celebrate my return than with a new video on the Argument Principle!

In this lesson, I derive the Argument Principle in complex variables, which relates the winding number of a complex function with respect to a traversal over a contour C to the number of zeros and poles of that function inside C.

This video will be particularly useful when it comes to proving Rouche's Theorem, which will be the next video coming up. Questions/requests? Let me know in the comments!

Pre-reqs: Every video before this one in my Complex Variables playlist: youtube.com/playlist?list=PLdgVBOaXkb9CNMqbsL9GTWwU542DiRrPB

Lecture Notes: drive.google.com/open?id=1W8E1xLxwECVX1VJjKNkCF5992W0bmRCs
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