The moment this gentleman made me understand the imaginary numbers i have literally got tears in my eyes. YOU ARE A GREAT HUMAN BEING SIR! GOD BLESS YOU!
@@anabeldoyle3586 Jesus Christ loves us all. For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline. 2 Timothy 1:7 NIV
I am a pretty old dude to be studying math, i came back to pre-algebra and saw 'i', which i vaguely remembered. after seeing all of the concepts in this video (sin, cos, etc) it is super clear to me now why they taught me 'i' in high school. Amazing explanation, for me. Though judging by the comments, I can see some guys in early high school that are being shown 'i' for the first time, without any idea about trig or calculus, this could be improved someway to make this imaginary completely understandable to grade 9 students. Excellent work! Any high school teacher introducing students to 'i' should require this video as homework.
Well they taught you the wheel 🎡 in precalculus because you're right the angles is the "momentum" angles in both the imaginary numbers fields in physics and also in relation to visual or spacing frames of relative motion or distances with the idea of times in dimensional depths. If you use Tangents at 90s you get the momentums which otherwise don't exist because they angle the spin direction it's coming in or going out. Its like catching a ball in midair and knowing where it's going to land, you got distance, depth, and time, motion. All the degrees.
I’m a grade 9 student, high school just started and I came across this video, I love math and science and understood most of the video so far, very well explained
@@edgar_eats_pi Jesus Christ loves us all. For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline. 2 Timothy 1:7 NIV
@Reelty Productions Jesus Christ loves us all. For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline. 2 Timothy 1:7 NIV
been out of school for decades and have literally no use for this. BEST EXPLANATION EVER. I came here after watching a stick figure animation where he was fighting math and (i) kept coming up and I had no idea what that was. after almost giving up watching other terrible videos and guides, tried your video and I feel extremely enlightened and happy. back in my day, these would all be "undefined". I remember that word. almost wish I was back in school to solve these and commit them to muscle memory. ty!
I came here because I needed a good introductory video for my students. This is indeed a good one. However, I wish the math teacher would start with the "why" and not the "how ". My students can already solve quadratic and cubic equations when I explain imaginary numbers. I usually let them solve either of the two and, ideally, one from a real-world example. Most importantly, I pick one that yields a solution with the square root of a negative number but has a real number solution and can be solved with some guessing. When they guessed the right solution, I then showed them how applying the concept of "i" would get them to the solution they had guessed previously. I had students who could already do all the stuff shown in this video, but they had yet to learn why they were doing it or what the problem was in the first place. Showing them the "why" first provides purpose and reason and leads them down the path of understanding there once was a problem that someone cleverly solved.
@@shawnd.8498 Jesus Christ loves us all. For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline. 2 Timothy 1:7 NIV
This was incredibly helpful, thank you so much. I'm starting a Calculus class in two weeks after not having taken a math course in over 10 years! Nervous but excited, wish me luck.
@@AKRGaming71 Jesus Christ loves us all. For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline. 2 Timothy 1:7 NIV
This was a great explanation. Good history involved to. I haven't done this stuff in over 30 years. A friend that I work with showed me his math homework because he knows I'm great with math, but it's basic I can't remember certain stuff. This triggered a lot of memories. Such as Sin X=1/Cos X and Cos X= 1/Sin X and Tan X = Sin X / Cos X and Cotangent X=Cos X/Sin X Which allows me to do a lot. It's slowly coming back. Thank you.
Sir you are powerful than others and really inspire me for curiosity of unknown staff. I have easily understood about “i” concept and application just as other introductions you presented. I am so joyful from my heart. Thank you Sir❤
Great explanation! Though things like "ignoring the sign" creates a lot of cogintive dissonance in my brain. I see it this way: If sqrt(a) = the number that multiply with itself to get a (which makes geometrical sense since the sqareroot then is the 'root'/line of the area of the square). Then using this rule: (a*b)^2 = a^2 * b ^ 2. So (2I)^2 = 2^2 * I^2 = 4*(-1) = -4, which fullfils the definition of a squareroot, and takes the sign into consideration.
I suggest that you put everything related to the radicals lessons in one group so that we can follow the lessons in order to make it easier for us. as well as exponents
This video got you a sub. It's very hard to find videos or resources that elucidate concepts like imaginary numbers well, but this is one of those. Thank you!
Thank you for this video. After watching this video, it cleared a lot of confusion surrounding the topic of imaginary numbers. Afterwards, I was able to apply my knowledge and practice what I have learnt. Thank you once again. It's always a great feeling when you finally understand a topic in mathematics.
Throughout high school, I was in "high honors" mathematics, so that by my senior year I was learning "advanced caculus" in preparation for the advanced placement exam. Which of the two exams I took, I do not remember, but I do remember this. The very existance of "imaginary numbers" was not revealed to me and my fellow traveling "high honors" math classmates until a month or so before we took the test (the year was 1975). I was so confused from misunderstanding imaginary numbers, I ended up scoring only a 3 out of 5 on the exam, even though, so far as I can remember, the test I took required NO understanding of imaginary numbers at all! I was devastated---prior to my teacher introducing "i" on the blackboard, I was among the top two, no more than three, students in my class! I was so ashamed, my life went in a completely different direction in college----I never took another math or science course again in my life. I wish I hadn't, because now my love of "Layman Physics", takes me only so far. I can read and understand books like "A Brief History of Time" by Hawking, or better yet, "Time Reborn" by Lee Smolin, but don't ask me to derive Schrodingers Equation, the Uncertainty Principle, or even E=Mc2. Nevertheless, I greatly appreciate the above tutorial. At least now I don't have to feel stupid if I were to run into a Physicist and ask him or her; 'when an observer causes the wave function to collapse, can it collapse to an imaginary or complex number, or is it always a "real" number'! (parenthetic pun intended)
Imaginary numbers have always been a bit of a mystery to me. I wish that I had teachers like this when I was in school. The use of the imaginary # I see is easy to understand after seeing this video. 👍👍
Its been a long time since I have had to use any of this. I enjoy your explanations and simplification of the subject. I would have done much better in cal with you as an instructor.
you could also show an example like this: (5i)^2 = 5i × 5i = 5× 5× i × i = 25 × i2 = 25 × −1 = −25 very simple example of how we get to a real number from an imaginary number (something a little more interesting than -1)
Genuine question here, because I got confused when he started doing the trees, if someone could please help out. At 23:08 he said 8x3=24, which is fine, but 6x4 is also 24, so it seems to fall apart there because then he wouldn't have his 2x2. What Rule am I missing? cheers.
It doesn’t matter it’s just preference really, he seems to prefer the factor tree method. If you look for the biggest perfect square which would be 4x6 the square root of 4 is 2 and 6 stays so it would still be 2 square root 6. :)
What gift, to learn from such teachers. Thank you seems so so lame. Soon I shall be able to buy your help, each month. I thank you for your service to us.
can someone explain me what is 1/4th power of -ve1 because 1/2nd power of - ve 1 is called or defined as i........ so the question is what's the 1/4th power of - ve 1 or 1/8th power of the same
Very good explanation. I do have a nit with your decimal expansion of square root of 2 at minute 37:59. It should be 1.414213... Having memorized this long ago, I kinda cringed. You left out the 2nd "4" digit.
The moment this gentleman made me understand the imaginary numbers i have literally got tears in my eyes. YOU ARE A GREAT HUMAN BEING SIR! GOD BLESS YOU!
Jesus Christ loves us all.
For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline.
2 Timothy 1:7 NIV
@@xan6990 Clown, STOP spamming.
@@JthElementI know you're not talking
This is the first time I am seeing a math professor combining with physics professor in one man.. Awesome....
You rock!!
@Blanch Bagnall okay wtf are you talking about
Absolutely!
He shows how mathematics applies in the real world as opposed to in a vacuum.
I love it!
Jesus Christ loves us all.
For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline.
2 Timothy 1:7 NIV
@@anabeldoyle3586 Jesus Christ loves us all.
For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline.
2 Timothy 1:7 NIV
I am a pretty old dude to be studying math, i came back to pre-algebra and saw 'i', which i vaguely remembered. after seeing all of the concepts in this video (sin, cos, etc) it is super clear to me now why they taught me 'i' in high school. Amazing explanation, for me. Though judging by the comments, I can see some guys in early high school that are being shown 'i' for the first time, without any idea about trig or calculus, this could be improved someway to make this imaginary completely understandable to grade 9 students.
Excellent work! Any high school teacher introducing students to 'i' should require this video as homework.
Jesus Christ loves us all.
For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline.
2 Timothy 1:7 NIV
Well they taught you the wheel 🎡 in precalculus because you're right the angles is the "momentum" angles in both the imaginary numbers fields in physics and also in relation to visual or spacing frames of relative motion or distances with the idea of times in dimensional depths. If you use Tangents at 90s you get the momentums which otherwise don't exist because they angle the spin direction it's coming in or going out.
Its like catching a ball in midair and knowing where it's going to land, you got distance, depth, and time, motion. All the degrees.
I’m a grade 9 student, high school just started and I came across this video, I love math and science and understood most of the video so far, very well explained
@@xan6990 what does have to with imaginary numbers?
I wish I had got a teacher/professor like you in my school/college I would have not struggled in my studies. You are a blessing. GOD bless you.
I get it. I get it. Thank you!
Excellent, effective, educative presentation style!
Jesus Christ loves us all.
For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline.
2 Timothy 1:7 NIV
What a great teacher.. I feel instead of attending school, kids should just watch his video. You are great!
Lol. I am 10 years old!
And I understand this!
School is to teach us and then give us practice, who will give us practice sheets of all we do is watch videos
@@edgar_eats_pi Jesus Christ loves us all.
For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline.
2 Timothy 1:7 NIV
@Reelty Productions Jesus Christ loves us all.
For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline.
2 Timothy 1:7 NIV
been out of school for decades and have literally no use for this. BEST EXPLANATION EVER. I came here after watching a stick figure animation where he was fighting math and (i) kept coming up and I had no idea what that was. after almost giving up watching other terrible videos and guides, tried your video and I feel extremely enlightened and happy.
back in my day, these would all be "undefined". I remember that word. almost wish I was back in school to solve these and commit them to muscle memory.
ty!
Truly, you explained/presented the complex world of math in its simplest manner! Math made easy! Thank you for all of your tutorial videos!!!
The Greatest.. Teacher of all times..
Love the class..
Wow perfect teaching, love how you show advanced math showing it’s use. Every class should do that
You brought significant clarity to this content for me. Thanks sir. ❤
Thank you so much. Wasn't understanding the concept of imaginary numbers on Khan Academy, but you cleared it up thoroughly.
I loved this lecture! So clear and informative... Thank you!
I came here because I needed a good introductory video for my students. This is indeed a good one. However, I wish the math teacher would start with the "why" and not the "how ". My students can already solve quadratic and cubic equations when I explain imaginary numbers. I usually let them solve either of the two and, ideally, one from a real-world example.
Most importantly, I pick one that yields a solution with the square root of a negative number but has a real number solution and can be solved with some guessing. When they guessed the right solution, I then showed them how applying the concept of "i" would get them to the solution they had guessed previously. I had students who could already do all the stuff shown in this video, but they had yet to learn why they were doing it or what the problem was in the first place. Showing them the "why" first provides purpose and reason and leads them down the path of understanding there once was a problem that someone cleverly solved.
You and Khan Academy are my two favorite resources for this kind of information. Thanks for everything!
NancyPi and the Organic Chemistry Tutor are also great teachers as well.
@@shawnd.8498 Thanks!
@@shawnd.8498 Jesus Christ loves us all.
For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline.
2 Timothy 1:7 NIV
This was incredibly helpful, thank you so much. I'm starting a Calculus class in two weeks after not having taken a math course in over 10 years! Nervous but excited, wish me luck.
Thank you so much,sir. I am not a maths teacher and I have difficulty in explaining about it. Your explanation greatly helps me.
"There's a lot more depth from what's on the board" I think is a reference to how many many boards he has
xD
why do i hate every video this guy makes?
@@AKRGaming71 Jesus Christ loves us all.
For the Spirit God gave us does not make us timid, but gives us power, love and self-discipline.
2 Timothy 1:7 NIV
This was a great explanation. Good history involved to. I haven't done this stuff in over 30 years. A friend that I work with showed me his math homework because he knows I'm great with math, but it's basic I can't remember certain stuff. This triggered a lot of memories. Such as Sin X=1/Cos X and Cos X= 1/Sin X and Tan X = Sin X / Cos X and Cotangent X=Cos X/Sin X Which allows me to do a lot. It's slowly coming back. Thank you.
Sir you are powerful than others and really inspire me for curiosity of unknown staff. I have easily understood about “i” concept and application just as other introductions you presented. I am so joyful from my heart. Thank you Sir❤
Wonderful presentation and explanation of concepts!!!
This lesson was really good. I like how he combined various topics in math.
Very very interesting and inspiring 💐 Your lessons are far more thrilling than any thriller 😊
Thanks a lot ❤
Great explanation! Though things like "ignoring the sign" creates a lot of cogintive dissonance in my brain. I see it this way: If sqrt(a) = the number that multiply with itself to get a (which makes geometrical sense since the sqareroot then is the 'root'/line of the area of the square). Then using this rule: (a*b)^2 = a^2 * b ^ 2. So (2I)^2 = 2^2 * I^2 = 4*(-1) = -4, which fullfils the definition of a squareroot, and takes the sign into consideration.
I appreciate all of your content. Thank you. Wish you would have been my professor for college!
I love the great depth you go-to for all your videos
I suggest that you put everything related to the radicals lessons in one group so that we can follow the lessons in order to make it easier for us. as well as exponents
you are without a doubt the best math guy on youtube
This video got you a sub. It's very hard to find videos or resources that elucidate concepts like imaginary numbers well, but this is one of those. Thank you!
Thanks for the sub! And thank you for the nice comment!
Thank you, your lectures have been very helpful for me. You make math seem beautiful even to a non mathematian like me.
Thank you for this video. After watching this video, it cleared a lot of confusion surrounding the topic of imaginary numbers. Afterwards, I was able to apply my knowledge and practice what I have learnt. Thank you once again. It's always a great feeling when you finally understand a topic in mathematics.
Damn, i liked your content right here. keep up the good work man, good job.
It's nearly been a half a decade. Still I am enjoying the subject as if it was yesterday. ty.
Throughout high school, I was in "high honors" mathematics, so that by my senior year I was learning "advanced caculus" in preparation for the advanced placement exam. Which of the two exams I took, I do not remember, but I do remember this. The very existance of "imaginary numbers" was not revealed to me and my fellow traveling "high honors" math classmates until a month or so before we took the test (the year was 1975). I was so confused from misunderstanding imaginary numbers, I ended up scoring only a 3 out of 5 on the exam, even though, so far as I can remember, the test I took required NO understanding of imaginary numbers at all! I was devastated---prior to my teacher introducing "i" on the blackboard, I was among the top two, no more than three, students in my class! I was so ashamed, my life went in a completely different direction in college----I never took another math or science course again in my life.
I wish I hadn't, because now my love of "Layman Physics", takes me only so far. I can read and understand books like "A Brief History of Time" by Hawking, or better yet, "Time Reborn" by Lee Smolin, but don't ask me to derive Schrodingers Equation, the Uncertainty Principle, or even E=Mc2. Nevertheless, I greatly appreciate the above tutorial. At least now I don't have to feel stupid if I were to run into a Physicist and ask him or her; 'when an observer causes the wave function to collapse, can it collapse to an imaginary or complex number, or is it always a "real" number'! (parenthetic pun intended)
This is my third imaginary numbers vid and the first one where I’m understanding it thank you ✨✨
You’re welcome 😊
This is very great.
Really good explanation. Thank you🙏
Imaginary numbers have always been a bit of a mystery to me. I wish that I had teachers like this when I was in school. The use of the imaginary # I see is easy to understand after seeing this video. 👍👍
Perfect explanation, thank you!
Wish I had this guy for my math classes
After knowing and been through all this, I find the pesistance to force sense out of an impossibility, insane.
Thanks for the explanation, it was very clear and useful
Thank you for your service
Great teacher!!!
You are a great teacher!
Its been a long time since I have had to use any of this. I enjoy your explanations and simplification of the subject. I would have done much better in cal with you as an instructor.
Very helpful for reviewing things, and also interesting and engaging. Great video!
All of this for free, i lovveeee you
God bless you and your work
Thank you so much sir, may God bless you a long life, love from India
Where can I get the last part ?
Have you made any video about the sin(x)?
you could also show an example like this:
(5i)^2
= 5i × 5i
= 5× 5× i × i
= 25 × i2
= 25 × −1
= −25
very simple example of how we get to a real number from an imaginary number (something a little more interesting than -1)
This is helpful. I am happy I understand now the imaginary numbers.
I wish I´d had this guy as my math teacher when I was a kid.
Thanks for this video, i like all your videos math and science
Thank you, mr.
Thanks. From Bangladesh.
Is there a playlist for complex numbers chapter? Otherwise where could i find part 12 of this series?
Genuine question here, because I got confused when he started doing the trees, if someone could please help out. At 23:08 he said 8x3=24, which is fine, but 6x4 is also 24, so it seems to fall apart there because then he wouldn't have his 2x2. What Rule am I missing? cheers.
It doesn’t matter it’s just preference really, he seems to prefer the factor tree method. If you look for the biggest perfect square which would be 4x6 the square root of 4 is 2 and 6 stays so it would still be 2 square root 6. :)
THANK YOU...SIR...!!!
What gift, to learn from such teachers. Thank you seems so so lame. Soon I shall be able to buy your help, each month. I thank you for your service to us.
Thank you're the best
You're the best. Thanks.
This is my first time I watch a full video talking about math
Thank you very much
Fantastic video! Keep up the good work sir!
thank you!!!
Brilliant - 30 years after I first learned about imaginary numbers, I finally get it.
Does the power rule apply to imaginary numbers? @29:46 you wrote i^3=i(-1). Couldn’t you use the power rule and say i^3=3i^2=3(-1)=-3?
Question: if we raise i to 0 and Sr of -1 to 0 does that mean 1=1
You are awesome, thank you so much!
Thank you so much.
I love this guy
Very interesting
This teacher’s style is a 1,000 times better than the teacher I have.
Powerful stuff.
Thankyou sir!
Thank you sir
Thank you🌹
thanks great stuff
I like the future look at why things are important.
Wish my imaginary ‘70 Dodge Charger R/T became real
Well, you need two of them
@@Unkown242 but if you multiply them, if i^2 is negative 1, then the commenter would actually owe someone a 70 Dodge Charger R/T
Now's eye's smart. Thank ya
can someone explain me what is 1/4th power of -ve1 because 1/2nd power of - ve 1 is called or defined as i........ so the question is what's the 1/4th power of - ve 1 or 1/8th power of the same
GRACIAS MIL POR LA EXPOSICION...SALUDOS DESDE KITU-ECUADOR
Very good explanation. I do have a nit with your decimal expansion of square root of 2 at minute 37:59. It should be 1.414213... Having memorized this long ago, I kinda cringed. You left out the 2nd "4" digit.
Can u slow down a bit? We know u know the material.... but we don't.
love it❤️
x=1/4 x1/2
Good explanation
Thank you so much!
Jason, MathAndScience.com
thank you
Welcome!
Imaginary numbers are like the fourth dimension. Hard to imagine, but necessary to explain things.
Why don't you give cubic equations as an example, which is algebra, and moreover the origin of imaginary numbers?
you are saying sine(x) . are you talking angle x in radians?
why do you put " [ " after equal sign?
This is the “doorway” between exists and non-existence? Like thoughts being a most primitive form of existence?
I was wondering my whole life why was i sqr = -1 thank u so much
Nice sir
so, spirit number is also real ?
(5i)cube/i