Complex Numbers: Operations, Complex Conjugates, and the Linear Factorization Theorem

[@johnryan7661]

I've watched this whole series from the beginning and, as of this video, have surpassed all the mathematics I ever learned in high school. I always assumed this stuff would be out-of-reach for the rest of my life, but here I am at the age of 30 looking forward to trig and calculus. Thank you, Professor Dave!

[@yashjagani3914]

You're a life saver☺️

[@XxwolphyxX5776]

thank you my test on this is in three hours and i think i know what im doing now

[@Duchess_pearl22]

Me too😂😂

[@buttek4631]

Why lecturers making this too complicated dave u are my man 👍🏼

[@Creek-44]

yep im here too

[@daniyashah5632]

i got 4 out of 10 in my exam and now today at last i got the concept and your test at the end of the video was amazing i did it correct thankk you

[@ntandazo5404]

My broer you're blessing no student or researcher can deny 🙌🏽🔥 thank you once again

[@adoeri7159]

Good timing. Math exam on Monday

[@vugiiii]

hope all is well , its been 6yrs , i hope everything turned out great for you , hehe its my turn to have an exam on monday now , thats why im watching this vid rn😂

[@vize_vids950]

@@vugiiii Hope all is well. its a month but now its my turn 😂😂

[@MuorbuotKiir]

Your explanation is accurate sir😊

[@TrinityTwo]

Great videos. Do you have one on de Moivre's theorem?

[@Djrienkenya]

Thanks sana Mwalimu..

[@KungaTsering-r3t]

Wow sir ur video is that which is really useful for me .I check many videos on utube but I found ur and that was best 🎉😮 THANK YOU SIR

[@debanshideb2577]

Could you please do a video on arguments of complex numbers. It would be very helpful. 🙂

[@mushiphysics.262]

Much love from Tanzania

[@x1n3t1x]

Awesome vid! Thanks!

[@Kind-of-Into-Machine-Learning]

Thank you professor dave!

[@SunnatullaYoʻldashaliyev]

thanks for clear explanation

[@shankardascivil]

Very helpful information sir ❤❤

[@Shelly-f2]

I was crazy i studied calculus and calculus makes me crazy crazy? I was crazy once I was crazy i studied calculus and calculus makes me crazy crazy? I was crazy once

[@Someone-cr8cj]

a casual: i^2 =-1 me, an intelectual: j^2=-1

[@carultch]

That's just because i is spoken-for to stand for current, so its alphabet neighbor is used in its place.

[@olivergrim7634]

@@carultch python uses `j` for its complex number :P

[@arrogant_little_punk9701]

At 5:39 how did that 15 changed into 13 ? Is it because of 15 and (-2) ? = 13 😅

[@pinkfluffyleona]

15 + (-2) 15 - 2 13

[@arrogant_little_punk9701]

@@pinkfluffyleona thnx i was confused 😂

[@stacyD27]

Is the square root of -1 + or - i

[@ProfessorDaveExplains]

positive

[@stacyD27]

Wait... if there was a quartic polynomial with imaginary solutions. i squared is -1. How could that make a real solution?

[@truesanatani2892]

@@ProfessorDaveExplains how is it positive professor.. I mean you yourself have written -1 there.. i= square root of minus 1 i squared = minus 1..

[@ProfessorDaveExplains]

Yes, he asked if the square root of -1 was plus or minus i. It's positive i. Therefore i squared is -1.

[@carultch]

@@truesanatani2892 Like square roots of positive numbers, there are two square roots of -1. By convention, without specifying otherwise, we are interested in the positive imaginary square root of -1, which is +i, and which is CCW from the positive real numbers on the complex plane.

[@JanuFlorido]

Its really odd to see this guy completely obliterate people that he doesn't respect but show a really nice charm voice when educating lol

[@Cookiekeks]

I think it shows that he really cares about what he's teaching

[@asayilethindwa3209]

You have made my headache cease. Thank you professor

[@ElisabethKambinda]

It's helpful..thanks

[@mukulsurya42]

Without maths they nothing in the world 🌍 maths is important for every person

[@Zoe-vj4qo]

wow thank you so much

[@CookieMage27]

Is it weird that I a watching stuff on imaginary numbers recreationally?

[@Cookiekeks]

Not weird, you're just naturally curious

[@petznassloukas7124]

that's nice

[@mustafasaber5076]

8 + i 2 + 4i 20 + 16i 11 / 17, 7i / 17

[@Lordsvessel979]

Wow thanks ❤❤😊

[@michelle-om9no]

thank you!!

[@AlessandroZir]

thank you!! clear explanations;

[@amirjafar3615]

thanks

[@ahmedalmedel4106]

thanks 🙏🙏

[@urbestie4396]

In the last questions i still don't get it why it come up 2+4i in the subtraction questions when i try it it was 2+18i could u please tell me i think i made a mistake but where

[@bathtubanarchy]

I imagine you didn't distribute the negative sign across the second term. (6 - 7i) - (4 - 11i ), as the negative is outside the bracket, you have to distribute the negative sign across both terms in the second term. (6 - 7i) (-4 + 11i), then you can remove brackets and solve. 6 - 7i - 4 + 11i 2 + 4i

[@rva1945]

is it possible to multiply two complex numbers with the real and imaginary parts not zero and the result is zero (0+0i)?

[@RedRahiq]

No, ig.

[@1upppls]

Thank you for the explanation. It really helped!

[@bhumishreesoni8665]

Is 4th one is correct in comprehension?

[@bathtubanarchy]

The fourth question is correct, or at least, I got the same answer as the solution.

[@lanzamaxxing]

i hate maths i hate maths

[@nurakid2008]

When u start understanding math, u hate this guys that are being ignorant, and know math. It feels good, I don't want to be proud of it. Instead I hate it

[@CageCodeblack]

Then stfu. And don't come here💀

[@kittysan0w0]

SAKI PFP SPOTTED also REALLL

[@creatorattractor4189]

😂😂

[@thang8617]

Complex number using in billiard game dev. It use to find path of billiard ball

[@Biggie_Shorts]

Please how did you arrive at 20+16i😢

[@reya8433]

i love you

[@Biggie_Shorts]

How did you arrive at 2+4i😢

[@DontolKont]

Are you stupid bro?

[@Marpace]

6-4= 2 and -7i - -11i = -7i + 11i = 4i

[@omarel-nemr6506]

i didn't get why the number of solutions must be the same number of n

[@reasatprottoy7488]

X+1=5 How many solutions of this equation? One. that is x=4 X^2+1=5 by using the quadratic formula we get x= 2, -2 X^3-4x^2-x=-6 by using synthetic division we get (x-3)(x-2)(x+1)=0 .so x= -1,2,3 See any pattern?

[@elvisihuoma]

Interesting

[@RayV6]

Going for advance Mathematics

[@ضياءظاهر-ل2م]

Thank you need ageen

[@PaulMwenda-vs3ys]

❤

[@kellytitus7771]

If you are here because you're writing an exam soon let's gather here

[@iamrisa18]

I hv a test tmr 😅

[@youcan_change_handle_3june_]

im imsoniac now

[@wafualex7930]

this was in 12th and 11th now I'm in degree 😅

[@Zone_Ranger]

The imaginary part of a+bi is just b

[@ProfessorDaveExplains]

nope! if it was just b, it would be a real number, you need the i for it to be imaginary.

[@Zone_Ranger]

Complex Analysis by lang (4th edition) : book uses alpha=a+bi.... def: "The real number b is called the imaginary part of alpha, and denoted by Im(alpha)"

[@ProfessorDaveExplains]

well i don't know what that book is or what it's trying to say, but if you have 2 + 3i, the imaginary part is not 3, as 3 is not imaginary. 3i is imaginary, so bi is a pure imaginary number.

[@Zone_Ranger]

Complex Variables with Applications by Wunsch: "We say that a is the real part of z and that b is the imaginary part."

[@Zone_Ranger]

yes bi is a pure imaginary number whose imaginary part is b.

[@aaaaaa1137]

So “complex”!

[@riemanngeometry9266]

Imaginary number only exist if you travel faster than light

[@ProfessorDaveExplains]

you're thinking of imaginary time/space, due to the radical in the lorentz transformation equations. this is just good old abstract mathematics here!

[@harrisonbennett7122]

@@ProfessorDaveExplains wow

[@carultch]

There are plenty of applications of imaginary numbers that have nothing to do with faster than the speed of light. For instance, the impedance of a capacitor is -i/(2*pi*f*C), or as electrical engineers like to state it, 1/(j*omega*C), because i is already spoken-for to stand for current.

[@agentkosticka17]

Wtf is this 2010 intro

[@LukaeziNicky]

thanks a lot, I'm improving i

[@JosephAbuo-x5e]

❤