Complex Numbers - Basic Operations

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  • เผยแพร่เมื่อ 22 ธ.ค. 2024

ความคิดเห็น • 697

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  ปีที่แล้ว +81

    Complex Numbers - Free Formula Sheet: bit.ly/3YAyxZe
    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
    Next Video: th-cam.com/video/H8OQtxSRe_k/w-d-xo.html

    • @mudlegacy
      @mudlegacy ปีที่แล้ว +3

      love this sir 😉

    • @Kiniemyeuthuong
      @Kiniemyeuthuong 10 หลายเดือนก่อน +1

      1:00:00

    • @Kiniemyeuthuong
      @Kiniemyeuthuong 10 หลายเดือนก่อน +1


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

    • @Kiniemyeuthuong
      @Kiniemyeuthuong 10 หลายเดือนก่อน +1

      3±\|** -63 ****

    • @Kiniemyeuthuong
      @Kiniemyeuthuong 10 หลายเดือนก่อน +1

  • @Zion122
    @Zion122 3 ปีที่แล้ว +394

    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 8 หลายเดือนก่อน

      ne za chto

  • @manique6
    @manique6 ปีที่แล้ว +165

    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

    • @somerandomgirl-x3z
      @somerandomgirl-x3z หลายเดือนก่อน +1

      thank you!!

    • @eidenjanet7854
      @eidenjanet7854 หลายเดือนก่อน

      Thank you this is so helpful

    • @krakenvh1406
      @krakenvh1406 18 วันที่ผ่านมา

      I hope you have a good day

  • @ikeamala247
    @ikeamala247 11 หลายเดือนก่อน +39

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

  • @Mimi-xy1tu
    @Mimi-xy1tu 3 ปีที่แล้ว +181

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

  • @frostcatmeow
    @frostcatmeow 3 ปีที่แล้ว +1754

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

    • @deemperor9979
      @deemperor9979 3 ปีที่แล้ว +7

      Were u from

    • @adamoja4295
      @adamoja4295 3 ปีที่แล้ว +10

      @@deemperor9979 Argentina

    • @deemperor9979
      @deemperor9979 3 ปีที่แล้ว +4

      @@adamoja4295 can i have your contact

    • @adamoja4295
      @adamoja4295 3 ปีที่แล้ว +36

      @@deemperor9979 bruh what for

    • @deemperor9979
      @deemperor9979 3 ปีที่แล้ว +26

      @@adamoja4295 we can be foreign friends

  • @zuggrr
    @zuggrr 3 ปีที่แล้ว +37

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

  • @emmanuellaamarachi
    @emmanuellaamarachi 2 ปีที่แล้ว +329

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

    • @Roba-U18
      @Roba-U18 ปีที่แล้ว

      i also noticed a mistake
      @@blackychan8570

    • @calebdakpala331
      @calebdakpala331 10 หลายเดือนก่อน +1

      Same

    • @PromiseUkonne
      @PromiseUkonne 9 หลายเดือนก่อน +23

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

    • @FeelGood-ph3mx
      @FeelGood-ph3mx 3 หลายเดือนก่อน

      😂😂😂👏👏👏

    • @Gadooraaabdelgader-pr1gh
      @Gadooraaabdelgader-pr1gh 3 หลายเดือนก่อน

      😂😂😂👌

  • @gageh3091
    @gageh3091 4 ปีที่แล้ว +363

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

    • @eyraiojeda9647
      @eyraiojeda9647 4 ปีที่แล้ว +4

      same

    • @charliechavez4374
      @charliechavez4374 3 ปีที่แล้ว +2

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

    • @colllo
      @colllo 3 ปีที่แล้ว +1

      It means you are like me

    • @ewandutoit7986
      @ewandutoit7986 2 ปีที่แล้ว +1

      FAAAAAXXXXXXX

    • @nonokiko738
      @nonokiko738 2 ปีที่แล้ว +3

      -9i

  • @kabouch
    @kabouch 4 ปีที่แล้ว +489

    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 4 ปีที่แล้ว +39

      I noticed that too.

    • @SwayzLandRecords
      @SwayzLandRecords 4 ปีที่แล้ว +27

      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 ปีที่แล้ว +29

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

    • @whosurbunny
      @whosurbunny 3 ปีที่แล้ว +8

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

    • @living._truth3270
      @living._truth3270 3 ปีที่แล้ว +2

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

  • @nathanvanlent9407
    @nathanvanlent9407 ปีที่แล้ว +21

    You doing more than most uni professors, absolute hero

  • @emmanuelconfidence723
    @emmanuelconfidence723 2 ปีที่แล้ว +522

    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 ปีที่แล้ว +8

      same

    • @manobrodeful
      @manobrodeful ปีที่แล้ว +45

      yes so the answer should be 11 - 9i

    • @equinox7189
      @equinox7189 ปีที่แล้ว +3

      Thank you.

    • @grapecraftfactions7675
      @grapecraftfactions7675 ปีที่แล้ว +3

      I noticed that too LOL

    • @craigasauruswrecks4915
      @craigasauruswrecks4915 ปีที่แล้ว +10

      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!

  • @Chnbl
    @Chnbl 3 ปีที่แล้ว +32

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

  • @samuelbaya8507
    @samuelbaya8507 2 ปีที่แล้ว +15

    thank you very much. I was thinking that i would be discontinued from my studies because of my poor grades but thanks to you awesome lectures which have changed me and raised me from zero to hero. GOD BLESS YOU

  • @janethflores9520
    @janethflores9520 3 ปีที่แล้ว +70

    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.

  • @gloryelizabethafuaakoto518
    @gloryelizabethafuaakoto518 2 ปีที่แล้ว +21

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

  • @macaronus3032
    @macaronus3032 3 ปีที่แล้ว +194

    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

    • @andrewwatts1997
      @andrewwatts1997 3 ปีที่แล้ว +9

      So how did the test go ?

    • @thedivineslayer1301
      @thedivineslayer1301 3 ปีที่แล้ว +2

      @@andrewwatts1997 ^^

    • @Bvngee
      @Bvngee 3 ปีที่แล้ว +2

      @@thedivineslayer1301 ^^

    • @macaronus3032
      @macaronus3032 3 ปีที่แล้ว +67

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

    • @justinblair9661
      @justinblair9661 3 ปีที่แล้ว +5

      @@macaronus3032 excellent job!

  • @aida-rz8uy
    @aida-rz8uy 4 ปีที่แล้ว +171

    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 ปีที่แล้ว +11

      Did you survive my friend?

    • @jonathan-ww3sx
      @jonathan-ww3sx 3 ปีที่แล้ว +23

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

    • @Aminahn11
      @Aminahn11 3 ปีที่แล้ว +6

      @@jonathan-ww3sx 𝚁𝙸𝙿☹︎

    • @InfoBinger
      @InfoBinger 3 ปีที่แล้ว +6

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

    • @black_crest
      @black_crest 2 ปีที่แล้ว +3

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

  • @antiscorbutic
    @antiscorbutic 3 ปีที่แล้ว +34

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

  • @crescendowook1733
    @crescendowook1733 3 ปีที่แล้ว +11

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

  • @michz9304
    @michz9304 3 ปีที่แล้ว +15

    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

  • @Ashley-ju8pc
    @Ashley-ju8pc 3 ปีที่แล้ว +26

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

  • @qwesiadvice8189
    @qwesiadvice8189 2 ปีที่แล้ว +12

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

    • @Omlet.official
      @Omlet.official ปีที่แล้ว +3

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

  • @loatilelebala6749
    @loatilelebala6749 3 ปีที่แล้ว +39

    POV: Your professor's notes and lectures are too long, don't make any sense and you have less than 48 hours until the exam.
    Thanks OCT, you are a real one!

    • @JimohAyomide-fg1bg
      @JimohAyomide-fg1bg 7 หลายเดือนก่อน +1

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

  • @8bpnoobie832
    @8bpnoobie832 3 ปีที่แล้ว +5

    I dont know how i can show u my respect and admiration i have for you. I am so thankful. I will be your premium user when i graduate.

  • @tommokloeck2395
    @tommokloeck2395 9 หลายเดือนก่อน +4

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

  • @justshan2413
    @justshan2413 ปีที่แล้ว +3

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

  • @tech_info9001
    @tech_info9001 3 ปีที่แล้ว +4

    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.

  • @davidchikamnaefe9006
    @davidchikamnaefe9006 ปีที่แล้ว +8

    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...❤

  • @rimberse3405
    @rimberse3405 3 ปีที่แล้ว +31

    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 😭

  • @georgesadler7830
    @georgesadler7830 2 ปีที่แล้ว +3

    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.

  • @Nxluda
    @Nxluda ปีที่แล้ว +2

    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.

  • @faraidhokoteramoyo7723
    @faraidhokoteramoyo7723 3 ปีที่แล้ว +6

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

  • @georgesongwe267
    @georgesongwe267 ปีที่แล้ว +2

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

  • @chisengachisenga1683
    @chisengachisenga1683 ปีที่แล้ว +4

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

  • @ashkannasab7919
    @ashkannasab7919 4 ปีที่แล้ว +9

    You teach better than college, THANK YOU VERY MUCH!

  • @Etk333
    @Etk333 ปีที่แล้ว +1

    Literally a life saver man.. u don't even know how clutch this is

  • @divinesamuel9634
    @divinesamuel9634 3 ปีที่แล้ว +8

    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!!

  • @wallacetembo317
    @wallacetembo317 3 ปีที่แล้ว +6

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

  • @nyakuekastephenbar
    @nyakuekastephenbar 2 ปีที่แล้ว +12

    I don't mind skipping lectures anymore coz I know The Organic Chemistry Tutor will take me through. Big thanks!!!!

  • @rman6572
    @rman6572 4 ปีที่แล้ว +38

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

  • @edeltovilla2773
    @edeltovilla2773 2 ปีที่แล้ว +2

    My favorite tutor online!.

  • @trishtea
    @trishtea 3 ปีที่แล้ว +4

    TYSM FOR THIS!!!! YOUR CHEM AND MATH VIDEOS HELP ME OUT A LOT AND I REALLY APPRECIATE YOU

  • @Arshadrayyan._.
    @Arshadrayyan._. 21 วันที่ผ่านมา

    Thank you sooo much mate! I'm rn in high school about to get graduated it's open schooling, my last 2 math n physics i never knew how I'm gonna study I'm not interested in tutor or something, but it's all god's plan I found your channel I can't thank you enough my exams will be in May or April ngl I'm feeling confident! Thank you once again! 🤝🏼

  • @skymalton3503
    @skymalton3503 4 ปีที่แล้ว +4

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

  • @karabonetshiomvani8362
    @karabonetshiomvani8362 7 ปีที่แล้ว +120

    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 ปีที่แล้ว +4

      Yeah, I noticed that too.

    • @amandaarans2178
      @amandaarans2178 4 ปีที่แล้ว +9

      Exactly I thought i was going crazy I knew it yayyyyy

    • @nextifytechnologies9210
      @nextifytechnologies9210 4 ปีที่แล้ว +2

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

    • @thusonyati1956
      @thusonyati1956 3 ปีที่แล้ว +3

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

    • @Unkown242
      @Unkown242 3 ปีที่แล้ว +1

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

  • @hadialqattan8309
    @hadialqattan8309 4 ปีที่แล้ว +41

    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.

  • @DaelinTV
    @DaelinTV 2 ปีที่แล้ว

    dude everything you teach becomes so easy, i love you!

  • @GryffieTube
    @GryffieTube หลายเดือนก่อน +2

    I believe you made a small mistake at 24:28. The sqrt(-9) is surely 3i, not 9i? Thank you for all your brilliant videos, easy to follow and understand! It has helped me a lot!

  • @claramark-hz5db
    @claramark-hz5db ปีที่แล้ว +2

    You're more than a genius.
    Your videos are really helpful. Thanks so much.

  • @godswayzottor5555
    @godswayzottor5555 11 หลายเดือนก่อน +2

    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.😊❤

  • @hamarsali1060
    @hamarsali1060 8 ปีที่แล้ว +25

    you explain very well...thanks a lot

  • @mun-emafabia6707
    @mun-emafabia6707 3 ปีที่แล้ว +4

    I like everything about you. You make things look more simpler for me.

  • @dina_kpoplover18
    @dina_kpoplover18 4 ปีที่แล้ว +5

    I love all your videos. You are the best. Thank you for all lessons

  • @nsxlocalities
    @nsxlocalities 2 ปีที่แล้ว +2

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

  • @emediongumoh4335
    @emediongumoh4335 3 ปีที่แล้ว +5

    Your videos are life savers 🥺💕💕💕 Thank youuuu!!!!!

  • @lynngitau6245
    @lynngitau6245 2 ปีที่แล้ว +3

    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

  • @muhamadarya1006
    @muhamadarya1006 2 หลายเดือนก่อน +6

    24:54 why the √-9 is a -9, why not the 3i

  • @debadityasaha856
    @debadityasaha856 8 หลายเดือนก่อน +1

    Great video, I noticed a mistake in the problem (7 - √-9) - (-4 + √-36), the second step will be (7 - 3i) + 4 - 6i at timestamp 24:23, so the answer will be 11 - 9i. Thank you.

  • @icebear1465
    @icebear1465 3 ปีที่แล้ว +2

    Thank you so much for this, I wish you the best health and luck all the time! THANK YOU!!!!!!!!

  • @Nxx89
    @Nxx89 ปีที่แล้ว

    THANK YOU SO SO MUCH. You are the best tutor. You helped me with math and chemistry so much. If i didnt find your channel i would be failing

  • @mosesmpasaleya1938
    @mosesmpasaleya1938 ปีที่แล้ว +2

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

  • @kakayibeatrice6598
    @kakayibeatrice6598 5 ปีที่แล้ว +4

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

  • @c60_buckminsterfullerene
    @c60_buckminsterfullerene 2 ปีที่แล้ว

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

  • @CedrickC-x4b
    @CedrickC-x4b ปีที่แล้ว +1

    Wow😮,this man made mathematics look easier to me,may the Lord bless you,it helped me a lot

  • @carmelpule1
    @carmelpule1 3 ปีที่แล้ว +2

    I have been hearing about real and imaginary numbers for the last 85 years and since, as an engineering student, I understood it all so well, at a young age I came to the conclusion that there is nothing imaginary about imaginary numbers and they are real, as any real numbers, but we must no longer talk about the numbers, we must start talking about OPERATORS and hence all operators become real in engineering.
    Let us say we have a "car" as the basic item, then using the symbol (4) as an operator to operate on the car, we can write (4 cars) and this would mean that four real cars exist and we would place them on the horizontal ground bumper to bumper and we have four cars in line on the ground, as we know it.
    Now if we want to create a vertical pole using four cars, (4 cars). then in language form, we would say that "four cars" are rotated by 90 degrees with the ground and placed in line one about the other to reach the vertical length of (4 cars,) which is the same length as four cars placed horizontally on the ground but rotated by 90 degrees to form a pole of four. cars. No one will ever deny that the engineering activity to produce such a vertical structure is VERY REAL So as language is not good enough to describe engineering functions, let us say that as we chose the number (4) to refer to as an OPERATOR to increasing the number of conventional cars, horizontally placed on the ground, then we would refer to a ROTATION OPERATOR (j) as an OPERATOR which would rotate by 90 degrees anything that is written behind it as (j car). Hence, ( car) is a normal car placed horizontally on the ground, and a (j car) would be a car rotated at 90 degrees with respect to the ground. ( j j car) would be a car that has been rotated by two ninety degrees rotational operations, hence 180 degrees and this would mean in engineering (a car), which is upside down hence ( upside down Car).
    A ( j j j j car) would be a conventional horizontal car, rotated by four 90 degrees operations, hence one full rotation, so that the car will look as it started, a conventional car which has been spun by one full turn to regain its original placement. All this operation of rotation of items, whatever they may be, is a REAL ACTIVITY AND REAL ENGINEERING REACTIONS.
    So the symbol, ( j 4 BULLS) would mean four BULLS PLACED IN LINE AND THE LINE ROTATED BY 90 DEGREES to a vertical direction.
    So when we say " real numbers" we mean referring to " real operators". that would amplify the entities we are dealing with. Now " j" , which we call an imaginary number, is no imaginary operation, but it is A ROTATIONAL OPERATION OF 90 DEGREES ORIENTATION.
    All this comes about by the operation which is required to find the SQUARE ROOT OF A NUMBER, BUT NOW WE MUST DESCRIBE, " THE ACTIVITY THAT ACHIEVES THE SQUARE ROOT OF AN OPERATION" and not just the square root of a number.
    So here we go in real terms,
    Defining the SQUARE ROOT OF AN OPERATION AS, ANOTHER OPERATION WHICH WHEN MULTIPLIED BY ITSELF WILL RESULT IN THE FIRST OPERATION.
    If the first operation is a real amplification operation of 9, then the square root of 9 is 3, as 3 multiplied by 3 is 3. That of 4 is 2 as 2 multiplied by 2 is 4.
    If the first operation is a real amplification operation of 1, then the square root of 1 is 1, as 1 multiplied by 1 is 1.
    Now (minus 1), or (-1) happens to be 1 operated upon by a real rotation by 180 degrees or two ( 90 ) degrees rotations.
    Having defined the SQUARE ROOT OF AN OPERATION, AS ANOTHER OPERATION WHICH WHEN MULTIPLIED BY ITSELF WILL RESULT IN THE FIRST OPERATION. then the square toot of (-1) is A ROTATION OF 90 DEGREES ON A LENGTH OF MAGNITUDE 1.
    1, rotated by 90 degrees and then, rotated again by 90 degrees, becomes (minus one)= (-1).
    So the operator j is not an imaginary number and it is not to be called just the square root of minus one, but it is a real rotational operation of 90 degrees to any entity placed beside it.
    IT IS ALL REAL ENGINEERING OPERATIONS AND IT IS THESE ROTATIONS THAT LEAD TO OSCILLATIONS found in repetitive heartbeats, musical frequencies, ballet pirouette dancing, and rotations of shafts and propellers, steam, diesel and petrol engines and jet turbines and electronic oscillations, spinning wheels it is all REAL! Please, Stop calling (j) an imaginary number, as the square root of (-1) is a real operation of 90 degrees rotation.

    • @andrewsanau9983
      @andrewsanau9983 2 ปีที่แล้ว

      wow. 😮

    • @carmelpule6954
      @carmelpule6954 2 ปีที่แล้ว

      @@andrewsanau9983 Thank you. I hope that " wow " was not a frightening experience but a pleasant experience of understanding that "j" is a real operator and not an imaginary one, It is a beautiful elegant operator which made Engineering control systems range from stability to instability. Thank you for appreciating how I chose to explain the "j' operator as an engineering function.

  • @emay69
    @emay69 ปีที่แล้ว +2

    your videos are really helpful thank you so much. I will remember this channel and show it to my kids in future🤧

  • @superyamky
    @superyamky ปีที่แล้ว

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

  • @JohnMuriithi-y6i
    @JohnMuriithi-y6i 2 วันที่ผ่านมา

    Sir you a genius ,24:52 there's a mistake everyone makes a mistake thank you very much teacher for making this topic clear ❤❤😊

  • @greatolisah4603
    @greatolisah4603 3 ปีที่แล้ว +7

    You're a legend bro.

  • @tylerdavis2920
    @tylerdavis2920 4 ปีที่แล้ว +19

    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 3 ปีที่แล้ว +2

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

    • @cientifica9150
      @cientifica9150 2 ปีที่แล้ว +2

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

  • @plrangel7015
    @plrangel7015 2 ปีที่แล้ว +1

    THANK YOU so much for teaching. It’s easy to follow your instructions.

  • @Decymedia
    @Decymedia 2 ปีที่แล้ว +5

    I JUST WATCHED YOUR CLASS UNDER 5 minutes i was able to understand you enough thanks

    • @shaoniboss6627
      @shaoniboss6627 2 ปีที่แล้ว

      bro i am in class 5 (classes are yet to begin and i can still understand this man's vids this guy is truly a legend.

  • @lidia9951
    @lidia9951 8 หลายเดือนก่อน

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

  • @ehehet5801
    @ehehet5801 8 หลายเดือนก่อน +8

    Came to the comments to know if anyone else also noticed the mistake. The 9i one.👍🏻

  • @yoorita8897
    @yoorita8897 2 ปีที่แล้ว +2

    Thank you very much... I could understand this topic so well, all thanks to you🙌

  • @evehong2944
    @evehong2944 2 ปีที่แล้ว +1

    24:46 Square root of -9 is 3i not 9i. You're confused me, anyway you're my best teacher so far. Thanks

  • @Sultan_A
    @Sultan_A 9 หลายเดือนก่อน +1

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

  • @Giantpro-sk8vd
    @Giantpro-sk8vd 10 หลายเดือนก่อน +222

    if you watching this video in 2024 like my comment

    • @terencejoel6205
      @terencejoel6205 8 หลายเดือนก่อน +5

      You ain't alone Brother

    • @Krageon-Offline
      @Krageon-Offline 2 หลายเดือนก่อน

      Shut up

    • @chuck1804
      @chuck1804 26 วันที่ผ่านมา

      No.

    • @Krageon-Offline
      @Krageon-Offline 26 วันที่ผ่านมา

      @ you failed by interacting with the comment and boosting it in the algorithm.

  • @turbobros_online1561
    @turbobros_online1561 3 หลายเดือนก่อน

    TY so much! You are helping me get ready for my algebra midterm. I'm really learning!

  • @Michealorina
    @Michealorina หลายเดือนก่อน +1

    ❤❤❤ you just made me love math more👏👏👏👏👏👏

  • @elvisdjango5920
    @elvisdjango5920 2 ปีที่แล้ว +2

    Massive appreciation for the good work. Thank you

  • @carmenjones7243
    @carmenjones7243 2 ปีที่แล้ว +1

    Thank you so very much for this resource. This helped me understand even with the errors. God bless you abundantly for taking the time to teach and helping others to learn.

  • @myworld_pure
    @myworld_pure 10 หลายเดือนก่อน

    Thank you sir for sharing your knowledge with us may the Lord reward you
    Easy method to get the i^ stuff is simply by doing this simple steps below
    EXAMPLE:
    If a question is given like i^4 in imaginary number ,if i is raise to an even number and the even is been divide by 2 and the answer still result to an even number we have the answer to the question as 1 i.e i^4=1 but if a question like i^6 is been given and the power is been divided by 2 and we got and odd number then the answer to the question i^6 will be -1

  • @vincentmuchimba7548
    @vincentmuchimba7548 3 ปีที่แล้ว +2

    The best tutor ever ✨✨

  • @giarichards1529
    @giarichards1529 3 หลายเดือนก่อน

    This dude is saving the world.

  • @mweshichanda6771
    @mweshichanda6771 2 ปีที่แล้ว

    My best tutor on TH-cam

  • @nigelgweru2695
    @nigelgweru2695 2 ปีที่แล้ว +1

    You are the one i should be paying my fees to,,,, You are great Mr

  • @gwenkapaipi
    @gwenkapaipi 5 หลายเดือนก่อน +1

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

  • @kassimmulla-jassim9766
    @kassimmulla-jassim9766 7 หลายเดือนก่อน

    this man carried me through 1st year physics

  • @igirl241
    @igirl241 3 ปีที่แล้ว +2

    For the problem at 47:01 . Isn't the conjugate supposed to be (5-12i)? you multiplied the top and bottom of the fraction by (-5-12i). Someone please correct me if I'm mistaken, thank you.

    • @jJo663
      @jJo663 3 ปีที่แล้ว +3

      No the conjugate is -5-12i. For example conjugate of a+b is a-b . so you only need to change the second part.

    • @kimchhoeu1638
      @kimchhoeu1638 3 ปีที่แล้ว

      Re arrange to make more easier to see, so, instead of -5 + 12i, it is the same as 12i-5, which you then multiple by conjugate: 12i+5

  • @aarondlama
    @aarondlama ปีที่แล้ว

    here just a few hours before exams learned so much thank you

  • @NashoenWray-p6s
    @NashoenWray-p6s 6 หลายเดือนก่อน +1

    Hello I must first say your videos are the best. I did notice that with one question where you were finding the square root of -9 you said it was 9i, is that correct? or should it be 3i. this is recorded at the time interval of 24:25s. please check.

  • @Moyinoluwa-wr1by
    @Moyinoluwa-wr1by ปีที่แล้ว

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

  • @michaelantunes9397
    @michaelantunes9397 7 ปีที่แล้ว +7

    You are amazing. Thank you so much. 👍

  • @annidoko9562
    @annidoko9562 ปีที่แล้ว

    Your videos are so comprehensive, thank you so much!!!

  • @IziPromise
    @IziPromise 3 หลายเดือนก่อน

    I haven't touched 2 of My Maths course work with more than 300 pages And I have the exam in 3 days time
    Bro just helped me cover it all in less than 5 hours 💀😭😂. BEST TUTOR FR!!🗿🗿🗣️🔥

    • @UnknownUserche
      @UnknownUserche 3 หลายเดือนก่อน

      yess! same lol
      what grade are you in?

  • @akannibasit
    @akannibasit 10 หลายเดือนก่อน

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

  • @adam_9787
    @adam_9787 9 หลายเดือนก่อน +1

    at 24:47 im just confused how you got -9i, wouldnt it be -3i? Thanks!

  • @YNDee1
    @YNDee1 2 ปีที่แล้ว

    You’re goated bro. I’m getting an A in my math exam tomorrow for you 😁