Complex Numbers (part 2)

[VDMiau]

Sorry, but where is the next video then??

[kbseeger]

how old are you? you sound like a college student haha

[TheYash76]

MY MATH GRADES DEPENDS ON YOUR VIDEOS..!

[3141Sal]

Damn I love this guy

[krayzai174]

if these videos were out when i was in school I would have made it into med school!

[sunnywinterx]

You simplify it so much that it becomes kind of annoying, I want some action with math ..

But I thank you for your great job .

[lacsapix]

I tryed this one (8-6i)/(4-3i) it has an interesting anwser

[frxstrem]

@lacsapix Well, it should be quite obvious why when you look closely: 8 is twice as much as 4, and -6 is twice as much as -3, therefore 8-6i must be twice as much as 4-3i.

[DrPsymotion]

@frxstrem no dude there is no comparison of complex numbers you can only compare their |X+Yi| lenght module or whatever it called on english there is no Z1>Z2 never fatal mistake only |Z1|>|Z2|

[frxstrem]

@DrPsymotion Though it is true that you generally cannot say that a complex number is "more" or "less" than another number, what I am saying is that when you double one of the complex numbers, you get the other; that's not comparing, that's multiplying by the real number 2 (which in turn is the same as multiplying the real and imaginary parts by this number). And by the way, I think the term you're looking for is the absolute value of a number.

[DrPsymotion]

@frxstrem true true (absolute value right thx) . and your point on the x2? what do you mean?i stil dont get how a complex number could be twice as much as another

[frxstrem]

@DrPsymotion The definition of "twice" is that a number (be it complex or real) times 2 is a number which is twice as much, or, that the second number divided by the first, is 2. And if you multiply a complex number by two, you'd get both the real and imaginary part doubled. There is no reason why doubling a number only should apply to real numbers; in fact, since all real numbers are complex numbers too, you could do the same to these, although you'd get no imaginary part as you'd multiply 2*0i

[DrPsymotion]

@frxstrem wrong 2*0i=0

[frxstrem]

@DrPsymotion ....that was exactly my point....

[me31192]

i have math exam tomorrow,it talks about this thing,anyway wish me luck^_^

[strknightt]

thumbs up if you have a test on this.

[ab94a]

I learnt more in these 10 minutes, than wat I have learned in a whole lesson in school...

[Kylehua14]

dat waz amazing!

[EdsToTheRescue]

omg thnk you soo much! My teacher will not for nothing in the world correctly teach us this. Now i will ace this test. U've made it so clear on how to work it step by step. TAHNX AGAIN SOO MUCH!!

[MilitaryMan006]

he got paid 2 million dollars by google for his site...

[TheInterNGA]

Thanks so much for this video, your a great teacher!

Just after 4minutes and 30 seconds into this video I got Beady Squared Eyes.

(BDi^2, get it? ;))

Just kidding, but thanks alot, you're a good person :)

[curryeater259]

In the middle of a math test, i excused myself to go to the bathroom and was watching your video's off my iphone. You helped me pass my exam with a 96%.

Thanks a lot Sal

[kkssw]

Thanks!

[silaes94]

You are amazing thank you so much!! YOU ARE AWESOME

[MrBoy1020]

can u please tell me how to solve i^29

[duliptulip]

@MrBoy1020 You know i^4 = 1

therefore i^28 = 1

i^29 = i

..I think

[Gazeta2nd]

@duliptulip

you are correct

and i^30 = -1 and i^31 is -i

[aydin1703]

thank you to who ever put this video. (I have passed my exam by watching and learning the content of the video

THANK YOU

[MegaTaeyanglover]

wow you are really good at teaching! thanks a lot! i'm going to pass my entrance exam for sure! :D

[nish9833]

DAnke schon fur die video

[iWriteUinMyDeathNote]

i dont get it :"{

[Matterboy81]

if you were my teacher, i would pass my math exam tomorrow.

[guitar2snow]

HE MISSED A SPOT!!!!! DX

[ionrotaru7]

Thanks a lot !!! God bless you and the job you'r doing !

[UKGrahamUK]

not paying attention all year does pay off! haha, jk.... your the best, thanks a bunch man!

[sjdeforest]

Best math teacher I've ever had. I also have a crush on your voice;)

[SmileForPink]

@sjdeforest I have a crush on his voice too!!! (:

[RavellaMusic]

@SmileForPink I know what you mean. It's ubiquitous. I literally just went to turn off my speakers 'cos I was sure I wasn't listening to anything; I think I must have believed his voice was just kind of... part of the world. He would make a convincing dictator.

[kourosh41]

This man is the best teacher i ever seen

[alearg89]

I love you guys, you make learning so much easier and fun.... and i also freaking love algebra :)

Seriously you are AWESOME

[darksupernova01]

Wow, thank you! You are truly amazing! How do you cover such a wide variety of topics... polymath ?

[radutheskater1]

thank you sooo much. I think my maths term paper next Wednesday won't be so hard after all. You're amazing:)

[ksakarim]

Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx Thanx T

[persianqu33n]

Thank you sexy voice lol

[Rizmaestro]

very good video but i think using numbers instead of letters will help people to understand. Or that might just be me

[doinitforsatan666]

@Rizmaestro i agree

when theres more letters than numbers i get confused

[TheKinza99]

yummmy....

[shats44]

oh... i wish u was my Lecturer... was gonna get a Distinction...

[TrustInTheFallenTV]

This would be way easier to catch onto if you used numbers instead of vairable. But thank you, you made it soo much easier to understand.

[sssandeep619]

it is nice

[cheesemule]

Should it be c squared minus d squared instead of plus d squared? Or did I miss something?

Because (a + b)(a-b) = a squared - b squared.

[woohbasketball]

@cheesemule u missed something, i squared = -1 so it nullifies the minus, so it became a +

[quaidanator]

this is great im in algebra 1 and i understood all of this (all ways nice to get ahead... except when im told "there is no equal to the square root of a negative number)

[alexhamster1134]

soulful maths

[genciT5]

can you tell me , what software do you use , to write mathemtaics equations??

[cscwty]

Thank you very much!! I love it because you solved my questions about complex numbers!!!

[cellchat]

OMG, stop arguing about proving it wrong just think of 'i' squared as being -1 (thaTS A RULE!) shut up about it

[93Ronn]

Thanks man ... It's 1:17 am now and I am on the verge of pulling an all-nighter 'coz I have math exam tomorrow, and as usual, I know nothing of algebra, and I'm tired of failing every semester ...

But these videos on Complex numbers (and your trig vids) saved me, really .. I guess I'll be able to sleep well now and am quite confident that I'll NOT fail this time lol xD

Above all, I got to understand what math really is about, and I'm starting to get real interested in it. Greetings from India!

[8anonomous8]

Nice vid but the Difference of Perfect Squares rule means (a+b)(a-b)=a^2-b^2

so c^2+d^2 should have been c^2-d^2 and 4+9 should have been 4-9=-5.

Would have been nice to also include some stuff on complex numbers in polar form, thats really what i was looking for but i still really enjoyed your video.

[tomtahh]

@8anonomous8 Yes that is the right rule. He is not incorrect: What happens when you square i.. -1. Are you incapable of multiplying 2 negative numbers together? Or are you too focused on trying to prove things wrong that are infact correct?

[francemaster]

@8anonomous8 i square= -1 so the sign in the D number is changed

[edajyamMie11]

thanks... for posting this one...

it' s a huge help for my quiz tomorow...

[extremkid]

I got a huge exam tomorrow, thanks for the help

[BACUS666]

FYI, you're not dividing complex numbers, you're simplifying them.

[NonEternal]

lol man, this is weird.. i use youtube everyday, but never thought of actually using it for study :\

[quazarphazar]

I'm just learning this because I find it super interesting :D You're an excellent teacher!

[deyomash]

super cool :) i like you ;-)

and i heard of this stuff and read on wikipedia about it, but i never really understood anything, so thanks for uploading this ;]

[Zipst3r]

very helpful but i cant find part 3?

[eyeojo]

Thanks,

i

Enjoyed it

[gvn933]

you are very amazing for doing these videos! they help me so much :] and you are a much better teacher than my math teacher :D( not just cuz i can pause them but in general! no kidding. )

[XeroXenith]

Very nicely explained! Thank you very much :)

Now if only everything we had to learn was available on Youtube like this...

[MrSlippyBlade]

Wish i could find some help for the modulus and argument of complex numbers...

Thanks for all the help, in one day you stopped me from failing my math exam tomorrow :D

[garg654]

Why does multiplying by the conjugate work?

[0HellBlaze0]

because it makes the bottom numbers Real therefore its easier to simplify.... best explaination i can give. hell im struggling to thats why im on here :P

[SurvivalDudes]

im not great at math, sorry if my explination doesnt sound good, but ill try

soo, basically you end up with the square of the first number multiplied by the square of the second number.

ie: (a+b)(a-b) = a(a-b)+b(a-b) = a^2 -ab+ab-b^2 now, the -ab and +ab cancel out, so you end up with a^2-b^2

hope that makes sense

[SurvivalDudes]

sorry not square of first MULT by second, but SUBTRACTED

[DeeVineDeeva]

u should plug in integers rather than variables

[karlkarlkarl1234]

I know (a + b)(a - b) = a^2 - b^2

But, what is that called again?

"Difference between squares", or something?

[sifs4]

yep diffence of squares.

[Blueknightex]

Nice but do you have anything about the Argand Diagram?

[allottaforchina]

iknowright

god i love this stuff

[pure0pwnage]

wtf is going on in the comment section of this video?? hm?

i thought this is a math lecture, not physical examination lecture, right? rofl

[wIzZaRd4893]

Blueknightex I think that you are totally right!! I am SOOOOOOOO lucky that there are only 8 people in my advanced maths class and we all get along so well. I used to be so lazy and give up so easily but now that i have that class i realised that the only person thats gonna benefit me putting my arse into gear is me.(if that makes sense)Awsome vid, you remind me alot of my maths teacher.

Thats another thing you need. A really good teacher to get you interested and excited about the sibject.

[tymoney321]

@wIzZaRd4893 What's so bad about having other people benefit besides yourself? The way you should think is 'the only person that's going to hurt by not putting my ass in gear is me.', Benefiting more people shouldn't be seen as a punishment =P

[wIzZaRd4893]

Hahaha, what u say is very true but i didn't really word that phrase properly. What i meant was that i was the only one going to be crippled by not working to my full potential. Basically exactly what u corrected me on :) Glad u picked that out, thx. And im also glad that there's at least one other selfless person that isn't afraid of correcting others mistakes in a polite and mature way.

[Blueknightex]

Thanks a lot. I hate sitting in class. It's so boring and sometimes I give up so easily because when people get better marks than me during practice exams it's like

"Yup that guys so gonna top our class and the teacher has more faith in him than any of us who failed" kind of stuff that I hear from other people but I think I finally realised that it's not about proving anything to anyone, it's about proving yourself that you can do it. =)

[Mahhbadd]

3:10 don't you just hate when your teacher leaves a spot on the board. I just can't stop staring at it and I don't feel at ease LOL!

[farzero]

you need to discipline your mind, that is a very big sign of mental weakness.

[Mahhbadd]

Oh really? Proof?

[farzero]

Its obvious that you are weak minded, if a dot on the board of a lecture as badass as complex numbers distracts you. You are weak, when it all boils down to it, if you put me and yourself in a maze, each one of us wielding swords, I would completely massacre you, because my mind is just that sharper. Do you also want proof I have a big penis?

[nugg69]

you are fucked in the head.

[Mahhbadd]

That's not proof, and what does a maze and swords have to do with it. Your mind is sharper...hmm great. Must feel great to be 'sharper' than someone. Oh and I could care less about your groin.

It's funny cause I could stare at that dot and still understand the lecture. Must have not distracted me that much huh. You have a nice day.

[Blueknightex]

Just because you have that problem does not mean that your all mental and all that. It's kind of a sign that you easily get distracted but still if you can understant the lecturer properly then that's ok =)

[wIzZaRd4893]

umm... I think there is something seriously wrong with ur reasoning there. Why, if two people were trapped in a maze with swords, would they try and kill each other instead of working together and using there swords and "Sharp minds" to find a way out? U might wanna go see a psychiatrist or something about that sword massacring tendency. Also being violent and dominating is not a sign of mental prowess.. actually im pretty sure its part of being a psychopath.

[JohnnyCagePro]

@Mahhbadd crap my attention won't be the same at class again

[MegaNatification]

@Mahhbadd freak

[mtksbctk]

@Mahhbadd das bullshit

[SytheX10]

Awesome.

[XirianValeria01]

Thank you very much! T_T This has always been my weakness (due to carelessness and mental blocks haha)

You made us think of complex numbers as not too complex. I will surely pass the CETs!!!

[matt11281x]

Don't worry. Just pay attention in class and you'll understand this stuff when you get to it.

[adam1611]

ehhh,,,, don't understand a shit :D

(8th grade :D

[1690362]

thanks, Khan this explaination simplify my confusion in complex..

[zambobel]

dude.. keep on with your videos..! they actually helped me a lot! thanx

[Stalingrad17]

thanks Khan !

[hgeithus]

Your videos are great. I'd love to watch one about the polar form of complex numbers.

[solutionsby]

i love u

[prabhasairam]

you are a great teacher. thanks alot for helping me.

[amysis92]

hey this video is so great. i'm actually from germany, and this video is big help for me. thank you very much

[yrumadaturself]

u are the  bomb the mr.kickass khan

[Aglaopheme]

Reall really cool! You make it easily understandable and in the same time it's kind of entertaining.. Thanks a lot!

[csnuebi]

found my error today at university ...

the right formula is

z1/z2 = ((x1x2) + (y1y2)/x2²+y2²)+i((x2y 1)-(x1y2)/x2²+y2²

this one you can use with stupidly insert the right x and y .

[csnuebi]

i am using the formula

z1/z2 = ((x1x2)-(y1y2)/x2²+y2²)+i((x2y­1)-(x1y2)/x2²+y2²

its from a collection my professor gave me.

[csnuebi]

this calculate is wrong, it think ..

it must be

-4/13 + 1/13i

plz correct me, if i am wrong

[Raziel0182]

never use a formula when you can use simple algebra to solve a problem =)

Distributing the numerator:

(1+2i) * (2-3i)  = 2 - 3i + 4i - 6 * i^2

since i^2 = -1

2 - 3i + 4i - 6 * i^2 = 2 -3i +4i + 6 = 8 + i

so it's 8 + i for the numerator, whereas you have -4 + i for the numerator

FYI 1/13i is NOT the same thing as i/13

[tomjackwhu]

what grade is this maths.

can anybody give me an indication when they learnt this?

[amozoness6]

This seems like late 8th grade-early 10th grade.

Vague, I know.

[dan20melb]

year 11 (grade 11) here in Australia if your doing accelerated maths. (just basics like this) and then again in grade 12 doing Specialist maths

[faramarzmunshi]

THANKS THIS IS A GOOD VIDEO

[korrisha]

Wow professor or sir you ar good I am a mathematics major and need help too on the absolute value and inequalities at university level please make much more vids to help people like me you real good when my lecturer did this I did not understand at all :(( It left me depressed and youtube was my last hope and walla was able to get it really good and explained thoroughly and I am a junior teacher you did this real good trust me looking out for more now of course at university level okay please!!!

[kevin2671]

I am always falling asleep during these lectures, real help finding this on youtube!

[iluvbeaners]

thanks so much! i have a math final tomorrow and i had no idea how to do this, you are a real life saver!

[mofuman]

thanks =)

[matt9017]

You are really good at explaining this. Thank you. :)