I don't understand the need for so many complex calculations when it suffices to divide 360 ​​degrees by 5 and write down the 5 answers (unit-length vectors in the complex plane) in exponential form.

First off, super neat handwriting! I think the problem you faced with making a video to solve this equation is that it is too simple if you use the fifth roots of unity that folks here are suggesting; you'd be done in a jiffy. Maybe you could try a more complicated equation that leads to handling roots of unity as a sub-problem downstream.

В этой игре разума не хватает главного: показать как комплексные корни при возведении в пятую степень превращаются в 1.

There is definitely value to show there are 5 answers, the obvious solution without any calculation needed is 1, but the right answer is that there are 5 solutions.  To me, the teaching format used is very tedious.  The writer is constantly moving papers from left to right, back to right to left, then down, then back up, and then back down to proceed.  I think showing this solution using a blackboard would work better.  The other concept overlooked is the use of substitute symbols, in this case M was defined.  It would be good to explain when substitutes are useful, not just suddenly pull out M to proceed simply for the sake of solving this problem.

I knew 4 of the solutions were going to be tedious, but he prolonged it by going through the calculation again, instead of just showing the final 2 from inspection.

The straightforward way is to write x^5=e^((2π i k/5)*5),k=0,1,2,3,4 . Hence the 5 solutions are e^((2π i k/5), k=0 to 4 . Written
out these are the solutions given in the video. The advantage is that one sees the same way that the solutions of the equation
x^n =1  form a regular n-gon in the complex plane.

複素平面を使って幾何的に解決できると私は思いました。

Si lo hubieras factorizado como resta de potencias impares, explicando el principio base de la factorización, hubiera calado más hondo. A veces menos es más. Igual me gustó mucho la creatividad ❤

I love the algebra displayed 👍

Make a unity circle in the complex plane around 0 and divide that in 5 segments starting at 1 and you have all 5 solutions.

Iszonyat lassú, érthetetlen, zagyva levezetés. A komplex síkon geometriailag 1 perc alatt bemutatható a megoldás. Ez a videó a matematikai szépségek meggyalázása.

Thank you.

Достаточно записать 1 в форме e^(2πi) и не морочить людЯм голову. :)))

Lehet, hogy ez nem matematikusi gondolkodás, de az 1 az akárhányadik hazványon is 1. Úgyhogy nem értem a kérdést, vagy ez egy beugratás?!
Nem nézem most meg a videót, Aludni megyek, mert szerintem ez egy átverés. Annak jó. :😀

相反方程式（reciprocal equation）の解法、すなわち、方程式の係数が左右対称（回文状）になっている性質を利用して次数を下げる方法、ですね。丁寧な解説をありがとうございます。

この方法は低学年のレベル（数学の低レベル）でも解けるので、とてもわかりやすかった。私ならこの方法でしか解けない。

No te enriolles, x=1
Ya te hemosn tomado la matrícula para la próxima

even you analysed so complicate the number of lines may reach to the moon, the answer has only one - no choice
can we use a short method even from the decision in mind.   anyway, thanks for your kind sharing.

1以外に有り得ない世界にオレは生きてる😂

Вы незнаете даже математические термины