The Fundamental Theorem of Algebra

This video explains the Fundamental Theorem of Alegbra and gives an interesting visual proof.

The proof is adapted from a similar proof given in 'Galois Theory' by Ian Stewart.

[Zachariah-Abueg]

i don't know if you intended to do this, but your video style -- the fonts you used, the navy blue background, the minimum amount of stuff on the screen at most times -- made me nostalgic for old educational tapes i used to watch as a kid. veryyy nostalgic. it felt so similar to the bare bones and straightforward style of visuals and pedagogical approach in those tapes. wow. anyway, really great video. i agree with someone below about your pace, i was able to follow veryyy well. subscribed!

[spoperty]

I've spent an embarrassing number of hours on math youtube explainers, this might be one of the best. Perfectly paced to make me feel smart, simple language throughout, this is what explainers should be like.

[PRIYANSH_SUTHAR]

Glad to see more and more amazing mathematics channels are created and making amazing content. Almost feels like a revolution on youtube.

[copywright]

Very nice! Watching the vid rn and it’s always great to see people cover this topic. Especially as a thematic sequel to your previous videos. You push me to do better with mine!

[zalibecquerel]

I must say, the pacing of your videos is spot on. Slow enough so that I can remember everything, fast enough to keep me engaged.
Turns out I'm a "visual learner". I took a couple of postgrad subjects in data science this semester. I would have failed both if not for StatQuest videos. No, really. I could have saved thousands in student loans and dozens of hours by watching youtube videos.

[ingiford]

for c in the complex numbers, the equation y=c either has no roots or infinitely many. y=0 has infinite roots, while y=1 has zero roots

[marcelob.]

Very nice, thanks. I'd recommend including the name of your channel somewhere in your video (beginning or end most usually).

[wh]

I liked your fonts selection! It'll be good to know.

[trevorclinton]

I think you forgot to handle the case that a sub 0 is equal to 0. In that case r=0 does not have a winding number of 0 since 0 will be a root.

[eveeeon]

This video was fantastic, it just left me thinking, maybe it's the mathematical desire for rigour in me, I couldn't help but think at 4:22 do we need to show that the set of roots/factorisation is unique? Like, it feels obvious but something in me wants to explore that a bit more. Also, 7:10 again this feels obvious but I feel like there is an assumption that you can always divide one polynomial into another, like we're trying to show that it has n roots, and in doing so we use the fact we can always divide out a polynomial (one of its roots) and using this by induction, so in a way are we not assuming it has n roots to prove the same?

This is not a criticism, its far more of a praise because your video was good enough to get me thinking about these things, and idk if its worth exploring these ideas further in future.

[elshadshirinov]

A sub zero is a Mortal Kombat character. This proves everything

[mapwiz-sfyt]

Didn't you have to also show that the winding number couldn't decrease (and later increase) as r increased, which would have given our polynomial n+2k

[LogicalQ]

What if you set the limit to i?
r
0 ——> i

[CaesarsSalad]

0 = x - 4 is not linear, it's affine.