Introducing the Complex Plane

[@Mathelite-ii4hd]

This way you instruct math subjects is just fab. It's really blessing and it helps students to learn these stuff with passion and joy. you are an example of the teach everyone wants to have:)

[@ace1262]

wow. this blew my mind twice...first was our natural conception of numbers as a 1 dimensional line, hence the number line. second was complex numbers as numbers existing on a 2-dimensional plane, as if to say that said complex number is finite in its 2D realm, but limitless when seen in 1 dimension. just, wow. thank you for showing us how these concepts are related, now i know how our predecessor mathematicians felt when they discovered something new.

[@epicmorphism2240]

Quatenions

[@Qermaq]

Yes, now think how now you know numbers are not just 1-dimensional but can be 2-dimensional. But think - they could have any dimensiality. And as it happens quarternions (4 dimensions) and octernions (8 dimensions) are very useful in STEM.

[@shmerox7683]

@@Qermaq yea totally. tho what about just 3 dimensional numbers?

[@Qermaq]

@@shmerox7683 You can do this, but it's not terribly useful. Look up William Rowan Hamilton and how he invented the quarternion set. Been a few KZbin videos on this.

[@strollco]

What an AMAZING job explaining this. Thank you so much. Your teaching skills are remarkable. I can't wait to teach this to my students.

[@finlaydunn3244]

Thanks for the vids man , love learning new thing an you make it so much easier.

[@Voy2k23]

The video was shot on my bday and its helping me on my final exams. The best bday gift ever.

[@kevinarmes9804]

Wow, I was kinda lost the whole time and mow I'm more confused than when we started. But in an excited kinda way. Awesome teacher!

[@Qermaq]

Watch it again. This is not that hard to get, but it is a sort of a mind blow.

[@surabhidixit1828]

you are an inspiration for me and thousand others. Keep up the good work

[@ArhamKhan05]

Thank You So Much Sir. Very much helpful, you taught it very beautifully and in a simple way. Love and Respect from Pakistan 🇵🇰.

[@amandeepsaha]

Best teacher, ever seen Thankyou Sir❤️ From india

[@bilbong6234]

Amazing teacher. Keep doing what you’re doing, man! Love this stuff

[@jasimmathsandphysics]

Cliffhanger resolved!

[@tracyosborne854]

Coherent, passionate and instructive. Thanks so much!

[@incognitoatious5443]

youre helping a ton of people and i appreciate that

[@akramnyangesse3644]

n Nice teacher.......................

[@cyrus2395]

Another absolute banger by Eddie Woo

[@krishanggoyal1534]

This is actually really helpful since I am doing IB math HL

[@matheusmeireles1781]

I wish my teachers had been Eddie

[@particleonazock2246]

Awesome video! Greetings from Pyongyang, North Korea!

[@Melesniannon]

Are they excited? *I'm* excited.

[@jontekkg7153]

I am having a really hard time understanding how the absolute value can be a real number when the point on y-axis is n*i units away from the origin while on the x-axis it is a real number of units away from the origin, I just don't understand how they can be added together to give a distance when they are two completely different things, can someone please explain?

[@jrc1156]

way back, I really imagined the complex numbers like mercenaries from other dimension that I can summon to the real world ( number plane) to defeat the monster (problem) :D

[@yoosufbelal9268]

These videos are brilliant, they're easy to follow and I hope you keep this channel going for as long as possible. Can you please help with the following question: A solid sphere, diameter 0.18 m, rolls (without slipping) down an inclined plane that is 6.00 m long. Find a) the angular velocity of the sphere at the bottom of the plane if it takes 12.0 s to reach the bottom and b) the angle of inclination of the plane in radians? Many Thanks

[@moat82]

Beautiful

[@whothedogwasdoing1846]

The class next door 💀

[@GooogleGoglee]

Beautiful! *i = +90° *(-i) = -90°

[@mehdimoussaoui1712]

Can we say that ℂ = ℝ² ?

[@AndresFirte]

Sort of. If you’re thinking about R^2 as vectors, then no. They are very similar. But Complex numbers can do one thing that you can’t with R^2 vectors: multiply. For example, I can multiply (2+3i)(6-4i). But I can’t multiply (2,3)(6,-4). However, if you choose to define a multiplication for the elements of R^2 as this: (a,b)(c,d) = (ad-bd, ac+bd) then you literally re-invented complex numbers. In other words, complex numbers are R^2 vectors for which you additionally defined a multiplication operation. Also in other words, R^2 vectors are just that: vectors. But Complex Numbers are vectors AND a ring AND a field (In simple words, a ring is something where you have a sense of addition and multiplication, and a field is a ring in which you also have a sense of division)

[@mehdimoussaoui1712]

@@AndresFirte Oh thanks a lot for your very complete answer. Makes a lot of sense!

[@toxickremedy]

WoW my education is complete garbage compared to this. It had never occurred to me that imaginative numbers are about another dimension. Insane. Would have been useful to know in highschool… doubt teachers knew

[@SaiCharannn]

Consider z = 1 + ai be a root of the polynomial p(x) = x4+10x2+ mx + 29, where a and m are real numbers. Determine the area of the quadrilateral whose vertices are the four complex roots of p(x) in the Argand-Gauss plane Pls help me

[@anthonylai7257]

i want to know if his students are subscribed

[@pelasgeuspelasgeus4634]

Does anyone really understand why the imaginary axis unit i has the same length with real axis unit? Also, the imaginary part of the CN is the product of multiplying the imaginary unit with a real number. Why the result is imaginary number?

[@AndresFirte]

Because the absolute value of the imaginary unit i is the same as the absolute value of the real unit 1. And the absolute value is a formalization of the intuitive notion of distance. So they are depicted as having the same distance to the origin to have a geometric intuition for them. The absolute value for complex numbers is a generalization of the absolute value for real numbers. And it is defined as |Z| = √(Zr² + Zi²), where Z is a complex number, Zr is the real component of Z, and Zi is the imaginary component of Z. And to the second question, because that’s what an imaginary number is: an imaginary number is the product of the imaginary unit i times a real number. That’s the name we have given to the set of the products between i and a real number. Perhaps if you look up the construction of the complex numbers using R² as the starting point it would be clearer for you

[@pelasgeuspelasgeus4634]

@@AndresFirte So, finally you admit it's an ARBITRARY CONVENTION that simply suits that twisted math fabrication you call complex numbers. Good for you. That means all graphs with CN are completely rubbish. By the way, will you finally explain why the multiplication of a real number with the imaginary unit results in an imaginary number? Also, you still owe me your thoughts on Kalanov's paper.

[@AndresFirte]

@@pelasgeuspelasgeus4634 ⁠I have literally always said the same thing: that it is how we depict it geometrically to give intuition and that that decision comes from the absolute value And I told you I’d give you my thoughts on Kalanov's paper once you give me a proof that √(a × b) = √a × √b, for a,b ∈ R or at least for a = b = -1. Because your whole “proof” that imaginary numbers lead to contradictions is based on that. The imaginary numbers are real numbers multiplied by the imaginary unit. It’s literally their name. That’s how we decided to call them. What do you think imaginary numbers are?

[@pelasgeuspelasgeus4634]

@@AndresFirte You literally use everywhere the same copy paste bs and you simply repeat that everything is a CONVENTION. Well, math have rules and you can't make your own suitable rules.

[@AndresFirte]

@@pelasgeuspelasgeus4634 if you keep asking the same questions then I’ll keep copy and pasting the answer. In fact, you basically copy and paste your questions. And yes, math has rules. But it also has definitions. And you asked a question about a definition. And definitions are (ironically by definition) conventions. Do you think that the term “imaginary numbers” was discovered under a magic rock? No. It’s two human invented words. Literally one day someone decided to assign the name “imaginary numbers” to the numbers of the form a×i where a is a real number. So if you ask why the numbers of the form a×i are imaginary numbers, then the answer is “because that’s literally how they are defined”

[@adedamolaalege1766]

Found it

[@helloworld-vq9gq]

In France, we learn this in High School

[@AdamLaMore]

He teaches high school, not university.

[@user-je9co6cr5i]

first, and WEAR YOUR FACE MASK ITS STILL COVID

[@GosuHub]

dawg, it's not your business.

[@vn88ttt]

There are at least 4 reasons that one can dislike your comment.

[@siddharthmohanty5731]

Its australia my guy.

[@RitobanRoyChowdhury]

Australia has actually done such a good job of stopping the spread that it's really not a big deal (and this video was recorded back in October. It's gotten worse recently, with Perth being back in lockdown), but when literally no one in the entire country has COVID, you don't need to wear masks. .