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
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
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
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
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.
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
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! 🤝🏼
Dear organic Chemistry tutor (Aka STEM JESUS). You’re videos are single-handedly the reason I passed majority of my high school classes and even in University. Every time I'm stuck on a subject, i feel safe knowing u already have a video that would explain it to me like i am a toddler that you made from 10+ years ago. Additionally when i watch them i cant help but be in awe of your amazing intellect and how ur better than most of these shitty proffs. I noticed your slight error in one of your questions but it just shows how much I learned from you and even you aren't perfect. May god bless you Sir.
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 😭
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.
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!
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.😊❤
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.
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.
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!
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!!
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.
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.
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
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
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 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.
Complex Numbers - Free Formula Sheet: bit.ly/3YAyxZe
Complex Numbers - Video Lessons: www.video-tutor.net/complex-numbers.html
love this sir 😉
1:00:00
❤
1
-
1
59-D3
226.01
سامسونگ
ا.
infinity
∞∞∞
3±\|** -63 ****
4±
This man is a legend. He explained it better than my college algebra teacher ever could. If you're reading this, thank you.
ne za chto
Even after 8 years your teaching is still relevant today thank you for this fine teaching
Honestly i need to meet this man and congratulate him on being the world best science tutor
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
thank you!!
Thank you this is so helpful
I hope you have a good day
You really deserve recognition for your works. You are one awesome teacher!! May God richly bless you
I noticed a mistake for once in my entire mathematics journey 😅 I'm proud of myself. Thank you
i also noticed a mistake
@@blackychan8570
Same
√9 = 3 not √9 = 9 please is that the mistake cause that is the . mistake I observe too?
😂😂😂👏👏👏
😂😂😂👌
Noticing the mistake means u learned from him. Don't forget to thank him :))
Were u from
@@deemperor9979 Argentina
@@adamoja4295 can i have your contact
@@deemperor9979 bruh what for
@@adamoja4295 we can be foreign friends
I think your teaching style of directly jumping into problems is great
learned more in 15 minutes (so far) than I learned the entire second sem. of alg 2. Thanks!!
same
Yesss its true man thanks to this guy appriciate the calm tone and time space between each explanation so clear...🖒👌
It means you are like me
FAAAAAXXXXXXX
-9i
You doing more than most uni professors, absolute hero
24:52 It is a mistake; the square root of 9 is 3; hence, 11-9i is the correct result of the subtraction
I noticed that too.
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
this show that we are concentrating .........i noticed that too
I caught it a well. Had 2 make sure I wasn't mistaken.
sqrt(9)*sqrt(9)*i(the squre root of -1) hes right
It's before 4 years but it still help the generation. Tnx dude.
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
same
yes so the answer should be 11 - 9i
Thank you.
I noticed that too LOL
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!
24:38 thank you sir. You made us understand the concept and realize the mistakes. Love from Ghana ♥️🇬🇭🇬🇭
I realised multiple questions wrong, but turns out It was because i did them wrong and he only made one mistake 💀
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
😮
You are a "one in a million" teacher. God bless.
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
So how did the test go ?
@@andrewwatts1997 ^^
@@thedivineslayer1301 ^^
@Strawberry Jam yeah I just wanted to tell everyone here that I managed to get an A+ I did it I passed
@@macaronus3032 excellent job!
6 years later I just want to thank you for clarifying this concept, keep going to higher limits
I watched it comletely till the end comfortably thanks to the clear and efficient explinations
Thanks!
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
Did you survive my friend?
@@mystilepo209 Looks like he passed out and never woke back up.
@@jonathan-ww3sx 𝚁𝙸𝙿☹︎
@@mystilepo209 Prob died like most Asian's do from sleep deprivation.
@@jonathan-ww3sx my condolences to his family. bro died studying math.
I’ve never had fun and understood so much in a math class before. Thank you sm!!
Same applies to me
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.
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
Dear organic chemistry tutor ....
I am grateful to God for making me come across ur videos. Thank you 😊
Just completed the entire video and have understood everything from it. I appreciate your willingness to educate us.
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! 🤝🏼
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.
My favorite tutor online!.
Wow.. So I can now see the mistakes... Thank you for being a wonderful teacher
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...❤
I honestly appreciate this...you make it so uncomplicated
Dear organic Chemistry tutor (Aka STEM JESUS). You’re videos are single-handedly the reason I passed majority of my high school classes and even in University. Every time I'm stuck on a subject, i feel safe knowing u already have a video that would explain it to me like i am a toddler that you made from 10+ years ago. Additionally when i watch them i cant help but be in awe of your amazing intellect and how ur better than most of these shitty proffs. I noticed your slight error in one of your questions but it just shows how much I learned from you and even you aren't perfect. May god bless you Sir.
Literally a life saver man.. u don't even know how clutch this is
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 😭
You teach better than college, THANK YOU VERY MUCH!
❤❤❤ you just made me love math more👏👏👏👏👏👏
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.
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!
√-9 is 3i . according to the first one you did sir thank you
The fact that I noticed your mistake means at the very least that your teachings are not falling on deaf ears.
THANK YOU!!!!!
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.😊❤
Came to the comments to know if anyone else also noticed the mistake. The 9i one.👍🏻
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.
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.
Your explanation is very easy to understand.... Am able to face the exam with confidence.... Thanks a lot, keep up with the good work
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!
Always the best,
Your videos are helping me during final exams.
Much thanks.
I don't mind skipping lectures anymore coz I know The Organic Chemistry Tutor will take me through. Big thanks!!!!
You the one I spend my time with all the time just as you did creating all these wonderful videos. May God bless you.
24:54 why the √-9 is a -9, why not the 3i
Mistake
dude everything you teach becomes so easy, i love you!
TYSM FOR THIS!!!! YOUR CHEM AND MATH VIDEOS HELP ME OUT A LOT AND I REALLY APPRECIATE YOU
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!!
learned more in the first 5 minutes than I did during a 90 minute class
You're more than a genius.
Your videos are really helpful. Thanks so much.
Thank you Sir. Using your videos I can study 1 hour before the test/exam. :-)
am really enjoying this lesson your opening my brain...
I hope I will be with you the entire time of course..
✨✨✨ Very Good, The Organic Chemistry Tutor, Keep It Up! ✨✨✨
24:46 Square root of -9 is 3i not 9i. You're confused me, anyway you're my best teacher so far. Thanks
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.
Yeah, I noticed that too.
Exactly I thought i was going crazy I knew it yayyyyy
@nicole peterson it is true, /-9 = (/9)(/-1) = 3(/-1) = 3i, in this case -3i
noticing the mistake mens you learnt something from him...
I immidiately went into comments thinking i may have gone crazy from studying 7 hours a day
I like everything about you. You make things look more simpler for me.
Your videos are life savers 🥺💕💕💕 Thank youuuu!!!!!
This explains my problem better than my teacher can explain my problem, thanks dude
Great video. Thanks!
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.
you explain very well...thanks a lot
Thank you so much for this, I wish you the best health and luck all the time! THANK YOU!!!!!!!!
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
I love all your videos. You are the best. Thank you for all lessons
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.
my thoughts right now as I stumbled on it .went here to see
@@mohameda.s5559 Same :D
Yeah that's -3i
Yaah there was a mistake
Thanks alot bes of you am gona pass my last year exams wow keep it up
your videos are really helpful thank you so much. I will remember this channel and show it to my kids in future🤧
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
My favourite teacher❤😊
You're a legend bro.
Wow😮,this man made mathematics look easier to me,may the Lord bless you,it helped me a lot
I swear this guy is the best at explaining stuffs to me about maths
THANK YOU so much for teaching. It’s easy to follow your instructions.
He made complex numbers simple. He's a hero.
Tomorrow I'm having an exam,i have learnt alot from you🙏 just hope it turns well,thank you 🥺
How the exam went
Sir you a genius ,24:52 there's a mistake everyone makes a mistake thank you very much teacher for making this topic clear ❤❤😊
Massive appreciation for the good work. Thank you
Thank you very much... I could understand this topic so well, all thanks to you🙌
TY so much! You are helping me get ready for my algebra midterm. I'm really learning!
Yeses mee toooo
The best tutor ever ✨✨
My best tutor on UA-cam
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
You are the one i should be paying my fees to,,,, You are great Mr
Your videos are so comprehensive, thank you so much!!!
I JUST WATCHED YOUR CLASS UNDER 5 minutes i was able to understand you enough thanks
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.
Really great content,I noticed the mistake something I have never done in maths. Good work sir
You are amazing. Thank you so much. 👍
May u continue to b rearded for all ur good deeds sir ur teaching is superb
i would go to sleep but i’m rlly interested rn
here just a few hours before exams learned so much thank you
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.
wow. 😮
@@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.
You’re goated bro. I’m getting an A in my math exam tomorrow for you 😁
Holy crap it makes sense now...thank you, thank you, thank you!
Thanks for the Explanation
Thank you . This is enormously helpful even after 4 years.