The geometric view of COMPLEX NUMBERS

[@somayazeidan131]

I came here just to say that I enjoyed learning with you , you are brilliant and you know how to make us love what we do ❤️

[@itzritam2127]

love from India. Your videos are really helpful for our engineering and statistical entrance examinations.

[@crimfan]

That's super clear and connects really nicely with the exponential representation because the angles add.

[@crimfan]

@@DrTrefor I figured that's where you were going but this setup of why complex numbers are indeed different from just any other vector space is super well-explained. The correspondence with a two-dimensional vector space that has an additional property is really clear.

[@MyMathsAdventure]

Moving onto Argand diagrams, the next chapter after Complex Numbers in my textbook. So great video to plugin any gaps before then 👍🏼

[@lavinnasays]

Oh my goodness. This video deserves way may more views. Thank you.

[@goalpost2326]

I just wanna appreciate your effort 💝 Good job Sir.

[@siddharthpandeyy]

Excellent way of explanation Sir.

[@itskarim7256]

Extremely underrated👏👏

[@eliasvandenberghe2196]

God damn, never thought anyone could entertain me with geometry.

[@nuhserkanelvanoglu7351]

The change of shirt was funny 😅

[@RubALamp]

Hey. Great video as always. You always deliver. However, have you considered investing in a mic? I don't mean to sound rude of course, but your videos could benefit with better audio quality. Thank you for your content!

[@RubALamp]

Trefor Bazett Of course I understand if it can't be improved at the moment. High quality audio can be a pretty expensive investment, and in the end it's only just a plus, nothing necessary. As stated, your videos are great regardless of the audio :).

[@crimfan]

@@DrTrefor A good podcasting mic on a mic stand would help a ton. Putting it in mono cardiod mode would catch your speaking very well. There are many of them available, though in COVIDpocalpyse they can be sometimes a bit hard to find. A mic stand is easy to get. An alternative might be one clipped to your shirt. I think there are wireless options available.

[@visualgebra]

So Helpful ever ....................

[@visualgebra]

@chidambaranathan s Fine brother

[@HDitzzDH]

So essentially, graphing complex numbers is the exact same as vectors in linear algebra, just plot each component in their respective axis.

[@johubify]

Great Video! I studied Complex Numbers in maths, and then Vectors in Details in Physics The resemblance between theme is shocking What's that about, can anyone explain?

[@johubify]

@@DrTrefor that is really true sir, but suppose we multiply 6+i to 6-i, we get 35 which is actually a real number in pure sense Now the thing that amuses me is that when we multiply two vectors we can either get a scalar or a vector Similarly, when we multiply two complex numbers we can get a real number or a complex number, making them really very similar! But all this is overshadowed by the fact that real numbers are a subset of complex numbers

[@physicslover1950]

@@johubify Yup nice approach thanks a lot.

[@johubify]

@@physicslover1950 you're welcome Physics lover

[@thingintresting5495]

8:50 no , multiplication by real number also results in Rotation. Check it by taking -1 and every number is a complex number as it can be represented in the Mathematical form of typical complex number.

[@katiatzo]

Thank you !

[@MikeyBarca02]

Short question, I'm a bit rusty with this so this question might sound a bit silly. But on 6:05 we called the horizontal length the cos and the vertical length sin. Now doesn't for example cos(alpha) tell us what the Adjacent side divided by the Hypotenuse equals? And that number is the ratio of the two and not the adjacent side only so why can we call the horizontal line the cos by itself?

[@physicslover1950]

Please also make a video on how to visually evaluate the powers of iota with shortcut and in an instant 💚

[@arsenalaman6493]

Wow its really amazing sir Thank you sir

[@Loots1]

you beat me :(

[@Loots1]

@@DrTrefor thank you good sir :)~ keep up the good work

[@wakeawake2950]

Do that trig property stands for more that 2 angle? By the way great video! 👌👌👍👍

[@ogunsadebenjaminadeiyin2729]

Great video. Merci

[@ogunsadebenjaminadeiyin2729]

The sound is hard to decrypt. You've got much bass (low/deep pitch) in your voice. You might consider using and (pre-)amplifier to fine-tune your audio.

[@reyadhalaraibi3529]

Great video!

[@zenicv]

I wish someone explained to me like this in 1st year electrical engg. class (noone did and now i understand)

[@happylife-lu7lo]

Great video, please can u make a course on number theory and thanks

[@physicslover1950]

Wao sir that was amazing . Thanks a lot. The strecting and conpressing concept was awesome . Sir I want to tell you that yesterday I read a topic of triangular inequality from the book of Dennis G Zill. It said that let z and z' be two complex numbers . Then |z+z'| < & = |z|+|z'| |z-z'| < & = |z|+|z'| |z-z'| > & = |z|-|z'| I think the last one is the most important result. This result must have a nice visualization . I hope if you also make a video in complex numbers playlist on this topic of mods | | . Well I have a good suggestion what if you can somehow download the pdf of FUN WITH TRIGONOMETRY by Vitthal B Jadhav. That book is very colorful and illustrates concepts visually. But unfortunately we can't afford that book. I would be very thankful to you if you either share me the pdf via email or make a video series on trigonometry after reading that book. 💚💚💚

[@christinanessie4428]

Hi, I think you meant to say green -1+2i instead of yellow at --4:43-- -- this threw me off a little

[@Anonymous-nz8wd]

Great video, but I have a question! why complex Eigen Vectors doesn't have invariant sub-space, according to the definition of Eigen Vectors it must be invariant or in the span but why not for Complex Eigenvalues?

[@vannya36]

i am also curios about it, did you find an answer to your question? If so, can you share it in your comment?

[@mr.p2665]

Shinuhowa e waaa

[@himanshuchauhan940]

I have a doubt , please anybody help me to resolve it ,why imaginary axis is is perpendicular to real axis

[@MrMarkgyuro]

what happened with your shirt at the end? :)

[@shivangisharma8429]

thankssssssssssssssssss