Complex Numbers - Basic Operations

This algebra 2 video tutorial explains how to perform operations using complex numbers such as simplifying radicals, adding and subtracting complex numbers, simplifying it in standard form, graphing complex numbers and calculating the absolute value of complex numbers. This video contains plenty of examples and practice problems. It's useful for students taking algebra 2, precalculus or college algebra.
Imaginary Numbers - Basic Intro:
• Imaginary Numbers - Ba...
Graphing Complex Numbers:
• Graphing Complex Numbers
Absolute Value of Complex Numbers:
• Absolute Value of Comp...
Adding & Subtracting Complex Numbers:
• Adding and Subtracting...
Multiplying Complex Numbers:
• Multiplying Complex Nu...
Dividing Complex Numbers:
• Dividing Complex Numbers
_____________________________________
Simplifying Complex Numbers:
• Simplifying Complex Nu...
SAT Math - Complex Numbers:
• Simplifying Complex Im...
Solving Equations With Complex Numbers:
• Solving Equations With...
Imaginary Solutions of Polynomials:
• How To Find The Real &...
Complex Numbers - Test Review:
• Complex Numbers - Prac...
______________________________________
The Discriminant:
• How To Determine The N...
Complex Numbers In Polar Form:
• Complex Numbers In Pol...
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 632

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor Жыл бұрын

    Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzread.info/dash/bejne/emyDs9axg7XLj84.html

  • @mudlegacy

    @mudlegacy

    9 ай бұрын

    love this sir 😉

  • @Kiniemyeuthuong

    @Kiniemyeuthuong

    5 ай бұрын

    1:00:00

  • @Kiniemyeuthuong

    @Kiniemyeuthuong

    5 ай бұрын

    ❤ 1 - 1 59-D3 226.01 سامسونگ ا. infinity ∞∞∞

  • @Kiniemyeuthuong

    @Kiniemyeuthuong

    5 ай бұрын

    3±\|** -63 ****

  • @Kiniemyeuthuong

    @Kiniemyeuthuong

    5 ай бұрын

  • @Zion122
    @Zion1222 жыл бұрын

    This man is a legend. He explained it better than my college algebra teacher ever could. If you're reading this, thank you.

  • @big8371

    @big8371

    3 ай бұрын

    ne za chto

  • @frostcatmeow
    @frostcatmeow3 жыл бұрын

    Noticing the mistake means u learned from him. Don't forget to thank him :))

  • @deemperor9979

    @deemperor9979

    3 жыл бұрын

    Were u from

  • @adamoja4295

    @adamoja4295

    3 жыл бұрын

    @@deemperor9979 Argentina

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    @deemperor9979

    3 жыл бұрын

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    @adamoja4295

    3 жыл бұрын

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    @deemperor9979

    3 жыл бұрын

    @@adamoja4295 we can be foreign friends

  • @emmanuellaamarachi
    @emmanuellaamarachi Жыл бұрын

    I noticed a mistake for once in my entire mathematics journey 😅 I'm proud of myself. Thank you

  • @user-je9xr4ez1u

    @user-je9xr4ez1u

    8 ай бұрын

    i also noticed a mistake @@blackychan8570

  • @calebdakpala331

    @calebdakpala331

    5 ай бұрын

    Same

  • @PromiseUkonne

    @PromiseUkonne

    4 ай бұрын

    √9 = 3 not √9 = 9 please is that the mistake cause that is the . mistake I observe too?

  • @emmanuelconfidence723
    @emmanuelconfidence7232 жыл бұрын

    I noticed a mistake here, where the square root of -9=9i Instead of square root of -9 = 3i But I really appreciate you alot on your videos It really helps me alot Thank you very much

  • @emmywlkr7611

    @emmywlkr7611

    Жыл бұрын

    same

  • @manobrodeful

    @manobrodeful

    Жыл бұрын

    yes so the answer should be 11 - 9i

  • @equinox7189

    @equinox7189

    Жыл бұрын

    Thank you.

  • @grapecraftfactions7675

    @grapecraftfactions7675

    Жыл бұрын

    I noticed that too LOL

  • @craigasauruswrecks4915

    @craigasauruswrecks4915

    Жыл бұрын

    came to the comments to look for this as I'm learning this as well and I was like, what am I missing, thanks for the confirmation!

  • @kabouch
    @kabouch3 жыл бұрын

    24:52 It is a mistake; the square root of 9 is 3; hence, 11-9i is the correct result of the subtraction

  • @charlottetlhabiwe5333

    @charlottetlhabiwe5333

    3 жыл бұрын

    I noticed that too.

  • @SwayzLandRecords

    @SwayzLandRecords

    3 жыл бұрын

    Thank you for confirming, I've been working the problems out before he answers them and I noticed he didn't use the perfect square for that one

  • @mauriceouma8454

    @mauriceouma8454

    3 жыл бұрын

    this show that we are concentrating .........i noticed that too

  • @whosurbunny

    @whosurbunny

    3 жыл бұрын

    I caught it a well. Had 2 make sure I wasn't mistaken.

  • @living._truth3270

    @living._truth3270

    3 жыл бұрын

    sqrt(9)*sqrt(9)*i(the squre root of -1) hes right

  • @manique6
    @manique67 ай бұрын

    00:00 Learn how to graph and calculate absolute value of complex numbers. 08:29 Simplifying square roots of negative numbers 15:17 Simplifying complex numbers and adding/subtracting them 21:59 Simplify complex expressions in standard form 29:57 Multiplying a complex number by its conjugate results in a real number. 36:55 Learn how to divide complex numbers 44:25 Complex numbers can be put in standard form using various techniques. 51:40 Solving quadratic equations with complex roots 58:50 Solving quadratic equations and complex numbers 1:05:56 Learn how to find the equation given imaginary solutions 1:12:27 Learn how to solve quadratic equations and find the sum and product of roots. 1:19:21 Sum and product of roots of a quadratic equation

  • @Mimi-xy1tu
    @Mimi-xy1tu2 жыл бұрын

    You really deserve recognition for your works. You are one awesome teacher!! May God richly bless you

  • @aida-rz8uy
    @aida-rz8uy4 жыл бұрын

    god i’m enormously tired and drowsy and i really just want to pass out on my bed right now but i would love to go over this topic before sleeping so one hour let’s fucking go

  • @mystilepo209

    @mystilepo209

    3 жыл бұрын

    Did you survive my friend?

  • @jonathan-ww3sx

    @jonathan-ww3sx

    3 жыл бұрын

    @@mystilepo209 Looks like he passed out and never woke back up.

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    @Aminahn11

    3 жыл бұрын

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  • @InfoBinger

    @InfoBinger

    3 жыл бұрын

    @@mystilepo209 Prob died like most Asian's do from sleep deprivation.

  • @black_crest

    @black_crest

    Жыл бұрын

    @@jonathan-ww3sx my condolences to his family. bro died studying math.

  • @Giantpro-sk8vd
    @Giantpro-sk8vd5 ай бұрын

    if you watching this video in 2024 like my comment

  • @terencejoel6205

    @terencejoel6205

    3 ай бұрын

    You ain't alone Brother

  • @gageh3091
    @gageh30913 жыл бұрын

    learned more in 15 minutes (so far) than I learned the entire second sem. of alg 2. Thanks!!

  • @eyraiojeda9647

    @eyraiojeda9647

    3 жыл бұрын

    same

  • @charliechavez4374

    @charliechavez4374

    2 жыл бұрын

    Yesss its true man thanks to this guy appriciate the calm tone and time space between each explanation so clear...🖒👌

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    @colllo

    2 жыл бұрын

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    @ewandutoit7986

    2 жыл бұрын

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  • @nonokiko738

    @nonokiko738

    Жыл бұрын

    -9i

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    @macaronus30323 жыл бұрын

    I will get an A+ on the exam just so all that time you spent to teach us doesn’t go into waste just watch I’ll make you proud

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    @andrewwatts1997

    3 жыл бұрын

    So how did the test go ?

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    @thedivineslayer1301

    3 жыл бұрын

    @@andrewwatts1997 ^^

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    @BvngeeCord

    3 жыл бұрын

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    @macaronus3032

    3 жыл бұрын

    @Strawberry Jam yeah I just wanted to tell everyone here that I managed to get an A+ I did it I passed

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    @justinblair9661

    3 жыл бұрын

    @@macaronus3032 excellent job!

  • @zuggrr
    @zuggrr2 жыл бұрын

    I think your teaching style of directly jumping into problems is great

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    @ikeamala2476 ай бұрын

    Honestly i need to meet this man and congratulate him on being the world best science tutor

  • @Chnbl
    @Chnbl3 жыл бұрын

    It's before 4 years but it still help the generation. Tnx dude.

  • @antiscorbutic
    @antiscorbutic2 жыл бұрын

    6 years later I just want to thank you for clarifying this concept, keep going to higher limits

  • @nathanvanlent9407
    @nathanvanlent94079 ай бұрын

    You doing more than most uni professors, absolute hero

  • @janethflores9520
    @janethflores95203 жыл бұрын

    This is really helpful though there some error, and I understand. This is not easy to take video lessons that is quite long, it cannot be avoided to have a small mistake. I salute the person who took time to share his knowledge for everyone to watch and learn that could be of help specially in this time of pandemic.

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    @samuelbaya8507 Жыл бұрын

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  • @theksmaster4097

    @theksmaster4097

    Жыл бұрын

    😮

  • @rimberse3405
    @rimberse34052 жыл бұрын

    Thank you for explanations. I wish my college professors explained like you do. Even though the examples you show are very basic it helps to understand the principle. But, unfortunately the problems that i get to solve for exams are 100x times harder 😭

  • @Ashley-ju8pc
    @Ashley-ju8pc2 жыл бұрын

    I’ve never had fun and understood so much in a math class before. Thank you sm!!

  • @mweshichanda6771

    @mweshichanda6771

    2 жыл бұрын

    Same applies to me

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    @gloryelizabethafuaakoto5182 жыл бұрын

    You are a "one in a million" teacher. God bless.

  • @rman6572
    @rman65723 жыл бұрын

    learned more in the first 5 minutes than I did during a 90 minute class

  • @Nxluda
    @Nxluda7 ай бұрын

    Holy crud this guy is an amazing teaching. Literally showing examples of every single step in solving the more complex problems before introducing those complex problems. I don't even need this for any class or project. I just ran into youtube short that used complex number and decided to look it up. GREAT WORK MAN.

  • @divinesamuel9634
    @divinesamuel96343 жыл бұрын

    This is very very effective, and I am so glad to have listened to your tutorial. It has really helped me. Thank you so very much @The Organic Chemistry Tutor. God bless you!!

  • @qwesiadvice8189
    @qwesiadvice81892 жыл бұрын

    24:38 thank you sir. You made us understand the concept and realize the mistakes. Love from Ghana ♥️🇬🇭🇬🇭

  • @Omlet.official

    @Omlet.official

    9 ай бұрын

    I realised multiple questions wrong, but turns out It was because i did them wrong and he only made one mistake 💀

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    @nyakuekastephenbar2 жыл бұрын

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    @faraidhokoteramoyo77232 жыл бұрын

    I honestly appreciate this...you make it so uncomplicated

  • @karabonetshiomvani8362
    @karabonetshiomvani83626 жыл бұрын

    thank you very much. well, I think you made one of those silly mistakes at 24:28 the third example of adding and subtracting complex numbers. you said the root of -9 is -9i instead of -3i. anyway thanks a lot I now know something.

  • @elijahafekode8255

    @elijahafekode8255

    5 жыл бұрын

    Yeah, I noticed that too.

  • @amandaarans2178

    @amandaarans2178

    4 жыл бұрын

    Exactly I thought i was going crazy I knew it yayyyyy

  • @nextifytechnologies9210

    @nextifytechnologies9210

    3 жыл бұрын

    @nicole peterson it is true, /-9 = (/9)(/-1) = 3(/-1) = 3i, in this case -3i

  • @thusonyati1956

    @thusonyati1956

    3 жыл бұрын

    noticing the mistake mens you learnt something from him...

  • @Unkown242

    @Unkown242

    3 жыл бұрын

    I immidiately went into comments thinking i may have gone crazy from studying 7 hours a day

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    @crescendowook17333 жыл бұрын

    Dear organic chemistry tutor .... I am grateful to God for making me come across ur videos. Thank you 😊

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    @loatilelebala67493 жыл бұрын

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  • @JimohAyomide-fg1bg

    @JimohAyomide-fg1bg

    2 ай бұрын

    √-9 is 3i . according to the first one you did sir thank you

  • @georgesadler7830
    @georgesadler78302 жыл бұрын

    MR. Organic Chemistry Tutor, thank you for a monster and mammoth explanation on the basic Operations of Complex Numbers. The examples cover all angles of Complex and Real Number Operations.

  • @justshan2413
    @justshan24138 ай бұрын

    Just completed the entire video and have understood everything from it. I appreciate your willingness to educate us.

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    @georgelishimba5027 Жыл бұрын

    This video has really helped me, thank you. After 6yrs the video is still help even to us learning it in 2023.

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    @8bpnoobie8323 жыл бұрын

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    @ashkannasab79193 жыл бұрын

    You teach better than college, THANK YOU VERY MUCH!

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    @davidchikamnaefe9006 Жыл бұрын

    Far better than my teachers here in Nigeria....much love would enjoy more of your content on chemistry in year 2 cause I'm a pharm student...❤

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    @michz93043 жыл бұрын

    Dear Organic Chemistry Tutor, I love you! Thank you so much for your videos. That's all. Love, A student who has been watching all your videos to pass a math exam

  • @hamarsali1060
    @hamarsali10607 жыл бұрын

    you explain very well...thanks a lot

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    @skymalton35033 жыл бұрын

    Thank you Sir. Using your videos I can study 1 hour before the test/exam. :-)

  • @tommokloeck2395
    @tommokloeck23954 ай бұрын

    I watched it comletely till the end comfortably thanks to the clear and efficient explinations Thanks!

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    @wallacetembo3172 жыл бұрын

    You the one I spend my time with all the time just as you did creating all these wonderful videos. May God bless you.

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    @dina_kpoplover183 жыл бұрын

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    @mun-emafabia67073 жыл бұрын

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    @icebear14653 жыл бұрын

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    @chisengachisenga1683 Жыл бұрын

    Your explanation is very easy to understand.... Am able to face the exam with confidence.... Thanks a lot, keep up with the good work

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    @Etk333 Жыл бұрын

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    @annidoko9562 Жыл бұрын

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    @plrangel7015 Жыл бұрын

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    @claramark-hz5db11 ай бұрын

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    @yoorita88972 жыл бұрын

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    @sanjayramharrack63546 жыл бұрын

    amazing stuff, thank you!!! ;)

  • @hadialqattan8309
    @hadialqattan83093 жыл бұрын

    You're the best, thanks a lot. btw, I think we've got a tiny mistake at 24:30, you said the sqrt(-9) = -9i instead of -3i.

  • @mohameda.s5559

    @mohameda.s5559

    3 жыл бұрын

    my thoughts right now as I stumbled on it .went here to see

  • @Youmni78

    @Youmni78

    Жыл бұрын

    @@mohameda.s5559 Same :D

  • @poramessianparapio9547

    @poramessianparapio9547

    Жыл бұрын

    Yeah that's -3i

  • @tech_info9001
    @tech_info90013 жыл бұрын

    I am not able to get membership of this channel and any paid video, but I just want to say you, sir, Thank you very much, You really saves many lives and I am One of them, The online classes are like shit, but sir your lectures is really make sense to understand, I am Thankful to you, Thank you very much. You are the best teacher in this whole world, Thank you very much, I was not able to study and One day I see your video and I just think you are only the best teacher for me, from beginning to last you put video and I was like dumb and not know anything, I just started from pre-algebra, and I am not dumb now, but many lessons are remaining, I think this time I really pass with my own words of theories and all hard maths sums in the exam of 12th standard, Thank you Very Much.

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    @kakayibeatrice65984 жыл бұрын

    Thanks alot bes of you am gona pass my last year exams wow keep it up

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    @michaelantunes93976 жыл бұрын

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    @davidjanovski54143 жыл бұрын

    Thank you a lot for your lessons it really helps me :D

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    @Nxx89 Жыл бұрын

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  • @nsxlocalities
    @nsxlocalities Жыл бұрын

    This explains my problem better than my teacher can explain my problem, thanks dude

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    @edeltovilla27732 жыл бұрын

    My favorite tutor online!.

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    @greatolisah46033 жыл бұрын

    You're a legend bro.

  • @lynngitau6245
    @lynngitau6245 Жыл бұрын

    There was an error in one of the questions where the square root was supposed to be 3i.but despite the error am so thankful because of the presentation it has really helped me a lot

  • @joshbrown8291
    @joshbrown8291 Жыл бұрын

    This is an amazing video. Thank you!

  • @simontilstedhansen9296
    @simontilstedhansen92963 жыл бұрын

    Great video! I learned a lot:)

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    @emay69 Жыл бұрын

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  • @c60_buckminsterfullerene
    @c60_buckminsterfullerene2 жыл бұрын

    He made complex numbers simple. He's a hero.

  • @lidia9951
    @lidia99513 ай бұрын

    Always the best, Your videos are helping me during final exams. Much thanks.

  • @georgesongwe267
    @georgesongwe2678 ай бұрын

    The fact that I noticed your mistake means at the very least that your teachings are not falling on deaf ears. THANK YOU!!!!!

  • @tylerdavis2920
    @tylerdavis29203 жыл бұрын

    I know of an easier way to do problems like i^10 (my algebra 2 teacher taught our class this neat trick) You just divide the exponent by 4 (since it is the highest out of the 4 i variables) and you use your remainder for your answer (in this case, the remainder would be 2, so it would be -1)

  • @shridharkhare0302

    @shridharkhare0302

    2 жыл бұрын

    That's the Basic way of solving here. I am amazed that you are being taught that as a trick!

  • @cientifica9150

    @cientifica9150

    2 жыл бұрын

    I knew this too! Very helpful for those who don't know, thanks

  • @sweetyvany99
    @sweetyvany995 жыл бұрын

    I watched the whole video. Good job.

  • @markkoni3499
    @markkoni34993 жыл бұрын

    thank u sooooo much!!! I LOVE ur vids, they are so helpful!!!

  • @pasqualedippolito3135
    @pasqualedippolito31353 жыл бұрын

    Congratulations all explanations are simple and clear.

  • @freeman0111
    @freeman0111 Жыл бұрын

    I'm so grateful to you , dude. Thank you infinitly.

  • @vincentmuchimba7548
    @vincentmuchimba75483 жыл бұрын

    The best tutor ever ✨✨

  • @chadafualo4742
    @chadafualo47422 жыл бұрын

    Thanks for the help making this topic easy to understand, thank you very much

  • @jemimaafiatwumasi5738
    @jemimaafiatwumasi57383 жыл бұрын

    I taught that i raise to power one is square root of (-1) but for the last example where i is raised to the power 201 (200 and 1), the answer should have been square root of (-1) but we got i. Can you please explain why?

  • @Ignoramus117
    @Ignoramus117 Жыл бұрын

    error at 24:50, -9 wasn't simplified 👍

  • @superyamky
    @superyamky8 ай бұрын

    I swear this guy is the best at explaining stuffs to me about maths

  • @amelia2534
    @amelia2534 Жыл бұрын

    Holy crap it makes sense now...thank you, thank you, thank you!

  • @felistuskabasiya1184
    @felistuskabasiya11842 жыл бұрын

    Thank you so much,, your teachings are really helpful

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    @ahmadb.e.k46294 ай бұрын

    I really appreciate your job. thank you.

  • @godswayzottor5555
    @godswayzottor55556 ай бұрын

    Appreciate your teachings . God really bless you abundantly in wisdom cause most of our lectures aren't that good enough in supporting our studies. Though I noticed a mistake which is the square root of -9 should be 3i not 9i and many more. Teaching is not an easy job.😊❤

  • @hibnibfnoeonjr
    @hibnibfnoeonjr2 жыл бұрын

    Thanks for the Explanation

  • @Moyinoluwa-wr1by
    @Moyinoluwa-wr1by7 ай бұрын

    Really great content,I noticed the mistake something I have never done in maths. Good work sir

  • @cammorale5114
    @cammorale5114 Жыл бұрын

    can anyone help, i dont understand 56:19, when i try to factor it i have a different and wrong answer, can anyone tell me why i cant use factoring in it and need to use the quadratic formula

  • @taba466
    @taba4663 жыл бұрын

    thank you .it really helped me to understand.

  • @papiz2090
    @papiz2090 Жыл бұрын

    Thank you so much. Subscribed!

  • @akannibasit
    @akannibasit5 ай бұрын

    May u continue to b rearded for all ur good deeds sir ur teaching is superb

  • @Sultan_A
    @Sultan_A4 ай бұрын

    ✨✨✨ Very Good, The Organic Chemistry Tutor, Keep It Up! ✨✨✨

  • @LuisMartinez-ly8xd
    @LuisMartinez-ly8xd6 жыл бұрын

    need help understanding how does 36 squared simplifys but 9 squared stays the same, at 24:50

  • @LuisMartinez-ly8xd

    @LuisMartinez-ly8xd

    6 жыл бұрын

    thx ur one of a kind

  • @consensusx2672

    @consensusx2672

    3 жыл бұрын

    Its a mistake

  • @SOEATSH
    @SOEATSH2 жыл бұрын

    This was awesome...mad respect💯

  • @MiriamUgwu-xj1hi
    @MiriamUgwu-xj1hi3 ай бұрын

    In a situation where there are two variables,how can I know when to compare the two equations or solve by substitution.

  • @abdul-kabirshittu8091
    @abdul-kabirshittu8091 Жыл бұрын

    Thank you so much. This was really helpful ❤

  • @mosesmpasaleya1938
    @mosesmpasaleya19389 ай бұрын

    am really enjoying this lesson your opening my brain... I hope I will be with you the entire time of course..

  • @hivir4654
    @hivir46543 жыл бұрын

    You saved my life,thanksssssss

  • @user-cj5cq1iq1f
    @user-cj5cq1iq1f4 күн бұрын

    Tomorrow I'm having an exam,i have learnt alot from you🙏 just hope it turns well,thank you 🥺