The Argument Principle | Complex Variables

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: https://www.youtube.com/playlist?list=PLdgVBOaXkb9CNMqbsL9GTWwU542DiRrPB Lecture Notes: https://drive.google.com/open?id=1W8E1xLxwECVX1VJjKNkCF5992W0bmRCs Patreon: https://www.patreon.com/user?u=4354534 Twitter: https://twitter.com/FacultyOfKhan Special thanks to my Patrons for supporting me at the $5 level or higher: - Cesar Garza - Alvin Barnabas - Aldo Mendes Martins - Yenyo Pal - Lisa Bouchard - Richard Mcnair - Guillaume Chereau - Patapom - Bernardo Marques - Jacob Soares - Otar Kemularia