Uploaded September 2019 | Updated September 2026, 2 weeks ago

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In this video, I prove Rouche's Theorem, which relates the zeros of a function f(z) and the sum of two functions f(z) and g(z), assuming that certain conditions are satisfied.

Following the proof, I apply Rouche's Theorem to an important example involving the proof of the Fundamental Theorem of Algebra. I'm sure that the pure math lovers who watch my videos will be excited to see this proof!

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=1Fm0RdZj5DAX460v8RvBrY0ilhYjBwhxg
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