Complex Numbers - Basic Operations

[@TheOrganicChemistryTutor]

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: kzbin.info/www/bejne/fmmygqeuiLeYlc0

[@mudlegacy]

love this sir 😉

[@Kiniemyeuthuong]

1:00:00

[@Kiniemyeuthuong]

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

[@Kiniemyeuthuong]

3±\|** -63 ****

[@Kiniemyeuthuong]

4±

[@Zion122]

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

[@big8371]

ne za chto

[@manique6]

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]

thank you!!

[@eidenjanet7854]

Thank you this is so helpful

[@ikeamala247]

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

[@frostcatmeow]

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

[@deemperor9979]

Were u from

[@adamoja4295]

@@deemperor9979 Argentina

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[@adamoja4295]

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[@deemperor9979]

@@adamoja4295 we can be foreign friends

[@emmanuellaamarachi]

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

[@Roba-U18]

i also noticed a mistake @@blackychan8570

[@calebdakpala331]

Same

[@PromiseUkonne]

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

[@FeelGood-ph3mx]

😂😂😂👏👏👏

[@Gadooraaabdelgader-pr1gh]

😂😂😂👌

[@Mimi-xy1tu]

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

[@emmanuelconfidence723]

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]

same

[@manobrodeful]

yes so the answer should be 11 - 9i

[@equinox7189]

Thank you.

[@grapecraftfactions7675]

I noticed that too LOL

[@craigasauruswrecks4915]

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!

[@zuggrr]

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

[@kabouch]

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

[@charlottetlhabiwe5333]

I noticed that too.

[@SwayzLandRecords]

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]

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

[@whosurbunny]

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

[@living._truth3270]

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

[@samuelbaya8507]

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

[@theksmaster4097]

😮

[@gageh3091]

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

[@eyraiojeda9647]

same

[@charliechavez4374]

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

[@colllo]

It means you are like me

[@ewandutoit7986]

FAAAAAXXXXXXX

[@nonokiko738]

-9i

[@macaronus3032]

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]

So how did the test go ?

[@thedivineslayer1301]

@@andrewwatts1997 ^^

[@Bvngee]

@@thedivineslayer1301 ^^

[@macaronus3032]

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

[@justinblair9661]

@@macaronus3032 excellent job!

[@Chnbl]

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

[@janethflores9520]

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.

[@nathanvanlent9407]

You doing more than most uni professors, absolute hero

[@crescendowook1733]

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

[@gloryelizabethafuaakoto518]

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

[@tommokloeck2395]

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

[@qwesiadvice8189]

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

[@Omlet.official]

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

[@georgesongwe267]

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

[@michz9304]

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

[@antiscorbutic]

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

[@aida-rz8uy]

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]

Did you survive my friend?

[@jonathan-ww3sx]

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

[@Aminahn11]

@@jonathan-ww3sx 𝚁𝙸𝙿☹︎

[@InfoBinger]

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

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

[@godswayzottor5555]

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.😊❤

[@justshan2413]

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

[@davidchikamnaefe9006]

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]

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 😭

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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.

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

[@debadityasaha856]

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.

[@Ashley-ju8pc]

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

[@mweshichanda6771]

Same applies to me

[@georgesadler7830]

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.

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

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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]

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

[@Michealorina]

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

[@lynngitau6245]

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

[@faraidhokoteramoyo7723]

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

[@evehong2944]

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

[@chisengachisenga1683]

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

[@mosesmpasaleya1938]

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

[@ashkannasab7919]

You teach better than college, THANK YOU VERY MUCH!

[@ehehet5801]

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

[@Nxluda]

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.

[@myworld_pure]

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

[@gwenkapaipi]

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

[@Gadooraaabdelgader-pr1gh]

How the exam went

[@edeltovilla2773]

My favorite tutor online!.

[@divinesamuel9634]

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!!

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

[@wallacetembo317]

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

[@karabonetshiomvani8362]

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]

Yeah, I noticed that too.

[@amandaarans2178]

Exactly I thought i was going crazy I knew it yayyyyy

[@nextifytechnologies9210]

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

[@thusonyati1956]

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

[@Unkown242]

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

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

[@skymalton3503]

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

[@takmkral7110]

24:30 square root of -9 is not 9i, it is 3i for those whom are confused

[@mun-emafabia6707]

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

[@claramark-hz5db]

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

[@carmelpule1]

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]

wow. 😮

[@carmelpule6954]

@@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.

[@kakayibeatrice6598]

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

[@rman6572]

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

[@emay69]

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

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

[@superyamky]

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

[@tylerdavis2920]

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]

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

[@cientifica9150]

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

[@c60_buckminsterfullerene]

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

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My favourite teacher❤😊

[@parththakor589]

i would go to sleep but i’m rlly interested rn

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

[@hadialqattan8309]

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]

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

[@Youmni78]

@@mohameda.s5559 Same :D

[@poramessianparapio9547]

Yeah that's -3i

[@ßtãñõmwãñgï]

Yaah there was a mistake

[@nsxlocalities]

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

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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

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

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

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

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

[@hamarsali1060]

you explain very well...thanks a lot

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I’m 11 years old and I understand calculus cause of you!

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the guy is so good i felt bad recognising hi mistake didnt even trust myself that I was right

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

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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.

[@nigelgweru2695]

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

[@GryffieTube]

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!

[@IziPromise]

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]

yess! same lol what grade are you in?

[@turbobros_online1561]

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

[@Gadooraaabdelgader-pr1gh]

Yeses mee toooo

[@eddiebussia5767]

The one that said (4+square root of -9) +(-4+ square root of -36) is supposed to be 11-9i not 11-15i, since 9 is a perfect square hence the square root of 9 should give you 3

[@yoorita8897]

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

[@pasindulakmal9778]

this is very help full thank you very much god bless you

[@carmenjones7243]

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.

[@Moyinoluwa-wr1by]

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

[@aarondlama]

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

[@emediongumoh4335]

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

[@infectia1965]

I think we can use the concept of cyclicity to find powers of i, let's say i⁷, divide the power, i.e. 7 by 4, the remainder is one of the first 4 ones you memorized, if you used a calculator .25 is 1st power, .50 is 2nd power, .75 is 3rd power and .00 is 4th power! Therefore i⁷ is i³

[@ZULUATRAI-kf8vf]

My name is Zulu Atrai . I like you way of teaching. I just want to point out the square root of （-9）should be 3j . this is my thought .

[@akannibasit]

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

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if you watching this video in 2024 like my comment

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You ain't alone Brother

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Shut up

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I really like your videos. I noticed that i^29=-1 instead of "i ".....I really love your videos it's really helping me

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i got a perfect score of adv engring mathematics quiz because of this video,thank you so much sir

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Massive appreciation for the good work. Thank you

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May the Good Lord bless you for pushing me through campus

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This dude is saving the world.

[@YNDee1]

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