It appears every real number has an imaginary state It appears that each number has a state of trig state corresponding to a value on the unit circle i = cos 90.
2.53 according to that property i square √-1*√-1 can be written as √-1*-1 and by multiplying it,we get √1 and we conclude it as 1 .this shows that i square is 1.please tell answer for this doubt...
the sums related to i can be done in a scientific calculators but before that we need to turn on the calculator on complex mode then it will show otherwise if it is in a normal mode(calculate) it will show invalid input or math error
Its positive 3i, cuz u have a rule, if u add the square root urself, its positive negative, but if its alrdy given in the question, then its only positive
Well, not telling it is a bad video. It is a nice and useful lesson! However, what I often observe is that it would be more fun if Indian math channels shift the overall perspective just a bit (I guess it is an Indian channel). 1. Focus more on the geometrical intuition than the numerical representation. It makes it easier for a student to grasp the material. And they won't need to memorize too much. 2. The intro to imaginary component should have come from i^2 = 1 instead of i = sqrt(1). Then it should have been extended to i = sqrt(1). 3. If it had been introduced with the proper geometrical intuition it could have been possible to say the right reason why it is called the unit component. The real reason is these points sit on the unit circle. 4. Although I did not have math at 11-12th, I am a hobbyist math learner. And I have observed a strange pattern among my friends and juniors, who had maths or currently studying math in high school, that they have never heard about the complex plane (organd diagram) and don't even have any idea of the changes that take places on the complex plane with each operation of complex numbers, for instance, the scaling and rotations of points with complex multiplications. Probably they will learn these in colleges. But understanding complex numbers without visualizing them is like memorizing arbitrary identities. Not to mention, that is in sharp contrary to the channel name. 5. There was only one instance in the video where they tried to draw something (1:40) but that was not even placed correctly following the complex plane. They could have placed the numbers ( 1, i, -1, -i) at their natural places. So, later when a student sees the complex plane they could feel a bit familiar.
We are really happy to hear that it was useful to you. We are glad that you understood the concept. You motivate us to do better. Keep watching our videos. 😊😊
#DidYouKnow: The product of two conjugate complex numbers is real. ✅To access all videos related to Complex Numbers, enroll in our full course now: infinitylearn.com/cbse-fullcourse?UA-cam&DME&KTNcYYHuBTY To watch more Complex Numbers videos, click here: bit.ly/ComplexNumbers_DMYT
If you really want to know the philosophy of Imaginary numbers, check my eBook at Amazon.com "Untold stories of Existence and Nonexistence True False: New Philosophy"
No. sqrt(-9) gives two results ±3i. Negative imaginary numbers exist as well. For example, the function f(x) = x² + 1 The fundamental theorem of algebra states that for any polynomial with highest power x^n, there are n roots (repeated roots included) So from x² + 1 = 0, x² = -1 x = ±√(-1) = ± i So to answer ukidding's question, yes there has to be a ± 3 at 3:06 .
It's actually because when it's x²+9 the ans could be 3 or -3 both it's because the quadratic rule you must have studied in class 9th that any quadratic polynomial ( where n=2) there are always 2 zeroes for that equation but here we don't need to put -3 because we have to find the value not to solve a quadratic equation
an easier way to imagine that imaginary numbers x real numbers is like even x odd even = imaginary odd = real numbers its easy by itself so this is useless and how much time did you waste to find this comment? edit: 0 is technically even so yeah
It is very wrong to proceed to describe a REAL ROTATING operator as something IMAGINARY when it is all so very real. The mathematical symbols we use are REAL OPERATORS including numbers and we must look upon them as such. (add) (subtract) (multiply) ( divide ) ( to the power) ( roots) ( the log of ) (reciprocal) ( proportional) ( areas , volumes and lines etc) all these are REAL OPERATORS and the reader may be surprised to hear that these operators do not only work on numbers but on entities............ we can multiply a chair by a table and get a related product. It is no wonder that written somewhere in an old book, humans as man and woman were told by God to " go and multiply" . Reproduction of any creature is the product of multiplication ! but we shall not go into that. We can have two and three dimensional multiplications to produce the most wonderful meaningful and non meaningful products. There is an operator which could be very useful to us and that is the ROTATIONAL OPERATOR which for the time being we shall call, " j ". To calibrate this operator we shall all agree that when we see the symbols " j " it will mean an anticlockwise rotation of 90 degrees , just purely a rotation to what it is associated with , while "( j^--1 or (1/j) ) is a clockwise direction. All these rotations will not interfere with the magnitude of the items that are rotated . so (car), j(car) , jj(car) , jjj(car) , jjjj( car) would mean that a car on its wheels, one which is facing vertically to the sky, another which is upside down, one which is diving down vertically , an another which has suffered a complete rotation of 360 degrees. Note that during these operations, the car remained the same size. This sort of notations is much shorter than using spoken and written conventional sentences to describe rotations around us including a growing plant as a spiraling vine growing grapes to make wine. In the real world items do not only grow and decay in straight lines but they do spiral and rotate around as they grow and decay. Now let us see the use of this rotation on finding the square roots. We shall define the square root as an operation, where when two exactly similar operations are conducted, then the product of this operation gives the result we want. We can define the cube root as an operations where when three similar operations are conducted, then the products of multiplying these three operations, will give the result we want. So if we take a pole one metre long pointing to the east described as say (pole) then doing a 90 degree rotating operating on it, now described as j(pole) this pole would be pointing North, while conducting another 90 degree operation described as jj(pole) well now the pole will be pointing to the west and we can say that jj(pole)= -(pole) and all this means that a pole operated on by two rotations each of 90 degrees will produce a pole pointing in the other direction . it is obvious that using normal algebra ( a pole ) on either side will cancel each other and hence jj= --1. All these ROTATIONS are REAL, VERY REAL, and so we shall not call a rotation of 90 degrees described by "j " an imaginary number for it is a REAL operation.
Is this some form of troll comment? I mean, no offence, but your maths is flawed. In what world will having two "poles", 1 metre in length each pointing in different direction yield -1? *a* - *a* = 0, we know this. *a* - *a* =/= -1. Let *a* be the vector of the pole, where -*a* is *a* but flipped about an end of *a*. If you mean the rotated pole alone being -1m long, I still don't see the link to complex numbers. Your description of what it means to find the square root may be confusing you. "We shall define the square root as an operation, where when two exactly similar operations are conducted, then the product of this operation gives the result we want. " - Firstly, we don't get results we want, when finding a square root, we use an input, and the outcome is what it is. Also, a square root is a number which when calculated yields a result which, if multiplied by itself, will produce the value we square rooted. Finally, "if we take a pole one metre long pointing to the east described as say (pole) then doing a 90 degree rotating operating on it, now described as j(pole) this pole would be pointing North, while conducting another 90 degree operation described as jj(pole)" is simply wrong. the first bit is right, using your function "j", but if you perform it twice, you have 2j, not jj, or j^2, so if you did use this function twice, the result would be -(pole), but that would not be equivalent to j^2 Also, they're called imaginary numbers because of their origin. From the sound of things, you're a theist, you believe things originated owing to an action (of God). Do you question why we call sticks sticks? They don't stick to anything, it's simply a word. It means nothing other than the thing that it is, it's a title, it literally allows you to identify it, that's all. The chances are, the people who are bothered enough with maths to know about the complex plane would not think that they dimply don't exist.
_Hey whoever you guys are I just want to say. I love you. In the sense of concepts. :-) :-)_
How you write italics
Yeah !!
U guys explain so good that i could understand it by looking at this only one's. Thanks
This is a nice video, and I link to it for my students. In place of your diamond I show my students a graph of 1, i, -1 and -i in the complex plane.
It appears every real number has an imaginary state
It appears that each number has a state of trig state corresponding to a value on the unit circle i = cos 90.
I really like your idea.
Cos 180
2.53 according to that property i square √-1*√-1 can be written as √-1*-1 and by multiplying it,we get √1 and we conclude it as 1 .this shows that i square is 1.please tell answer for this doubt...
the sums related to i can be done in a scientific calculators but before that we need to turn on the calculator on complex mode then it will show otherwise if it is in a normal mode(calculate) it will show invalid input or math error
Very very thanks of you it help me a big numerical analysis
Please make more videos on nda maths syllabus
Thank you so much .....this video is extremely helpful ☺️☺️
❤️
Yes
Thank u. Plz post videos on higher mathematics like real analysis algebra etc.
Thanks for send this video this video is really helpful.
does the mathematical property you wrote in 2:50 go back and forth?
If yes, why not √-1 x √-1 = √(-1x-1) = √1 = 1
BEST CHANNEL EVER SEEN ON UA-cam PLATFORM..............HATS OFF TO U MAM
Thank you for your kind words🙂
Please put more videos on vast topics
/a X /b = /ab ,if and only if a and b are positive. (/) is for root.
ch chaitanya no only one of them must be positive
That power trick of iota was awesome.. thank you
Cordial greeting.
Excellent video and very well explained.
Please could you tell me what program or application made the video.
I don't understand at school but now I done i power 2,3,4,5,7,8 but I didn't got i power 6 after that I got it thanks a lot for this channel
This video is very helpfull
Thank you it helped me a lot the video was short and we can understand by watching it once
Please solve this example in detail
i 888
i 116
i 403
Very helpful information sir ❤❤
Thank you maam.
Thank you so much for i concept
Can't we put directly -i= - [root of -1], in cube of i
I want to know that what is a value of i power half
Hy,
What is the value of i⁰
3:15 is it 3i or plus minus 3i?
Both r same
ı thought the same omg which one ıs correct?
Its positive 3i, cuz u have a rule, if u add the square root urself, its positive negative, but if its alrdy given in the question, then its only positive
plus minus 3i
Well, not telling it is a bad video. It is a nice and useful lesson! However, what I often observe is that it would be more fun if Indian math channels shift the overall perspective just a bit (I guess it is an Indian channel).
1. Focus more on the geometrical intuition than the numerical representation. It makes it easier for a student to grasp the material. And they won't need to memorize too much.
2. The intro to imaginary component should have come from i^2 = 1 instead of i = sqrt(1). Then it should have been extended to i = sqrt(1).
3. If it had been introduced with the proper geometrical intuition it could have been possible to say the right reason why it is called the unit component. The real reason is these points sit on the unit circle.
4. Although I did not have math at 11-12th, I am a hobbyist math learner. And I have observed a strange pattern among my friends and juniors, who had maths or currently studying math in high school, that they have never heard about the complex plane (organd diagram) and don't even have any idea of the changes that take places on the complex plane with each operation of complex numbers, for instance, the scaling and rotations of points with complex multiplications.
Probably they will learn these in colleges. But understanding complex numbers without visualizing them is like memorizing arbitrary identities. Not to mention, that is in sharp contrary to the channel name.
5. There was only one instance in the video where they tried to draw something (1:40) but that was not even placed correctly following the complex plane. They could have placed the numbers ( 1, i, -1, -i) at their natural places. So, later when a student sees the complex plane they could feel a bit familiar.
Pendyala education and entertainment channel👌👌
Thnk you
Nicely explained.
Thank you for such useful video
thanks
Well this property works if at least a or b is positive
This video was useful . 😊😊
We are really happy to hear that it was useful to you. We are glad that you understood the concept. You motivate us to do better. Keep watching our videos. 😊😊
#DidYouKnow:
The product of two conjugate complex numbers is real.
✅To access all videos related to Complex Numbers, enroll in our full course now: infinitylearn.com/cbse-fullcourse?UA-cam&DME&KTNcYYHuBTY
To watch more Complex Numbers videos, click here: bit.ly/ComplexNumbers_DMYT
But isn't
sqrt(1)=/=i^2
sqrt(-1)sqrt(-1)
=sqrt((-1)(-1))
=sqrt(1)
sqrt(1)=i^2
sqrt(1)=i^2 and sqrt(1)=/=i^2
But .. why will my dad ask that question ❓
Very usefull
Very good
By the way of what standard is this mathematics
11 India
@@satvikvarun6386 i asked this 2 years ago... now i am myself in class 11 and completed the complex numbers😆
@@ranendrachandrabhattacharj3229 that's awesomeeee. Btw I'm also in 11th now
nice video..thanks.
Nice explanation but low voice
Please translate this chapter in Hindi also thanks
Nice
Please do videos on qutranions.
Idot no do it by u r self
superbbbbb...👌👌👌👌
Thank you
Happy Learning :)
Where r u from
Vidyadhar Sharma Kmara
Hell
@@phimpand-thetamilinfograph6119 oh thanks😁😁
Super 🤩🤩🤩
Nice all video
😮 mathematics' vast
I like your videos
We are glad Harprasad that you liked our video..We hope that you understood the concept. For more videos, please visit our website - dontmemorise.com/
Nice mam
sqrt (-1) = error
If you really want to know the philosophy of Imaginary numbers, check my eBook at Amazon.com
"Untold stories of Existence and Nonexistence True False: New Philosophy"
What about i×0?
When i*0, means Im(z) = 0.
Hy,
What is the value of i⁰
good video lived it
Thank you :)
what if n=0?
sqrt (-9) = invalid input
I’m from Nowhere. U must professor
OM CALCULUS WHEN OM
I didn't understand that unit imaginary number.
Thanks
Comment no 101 great
Square root of -1 = error
: ) : ) superb video
at 3.06...the square root of 9 is 3......why not plus or minus 3?
Because ur dumb I think 3i and -3i are the same think a bit
No. sqrt(-9) gives two results ±3i. Negative imaginary numbers exist as well.
For example, the function f(x) = x² + 1
The fundamental theorem of algebra states that for any polynomial with highest power x^n, there are n roots (repeated roots included)
So from x² + 1 = 0,
x² = -1
x = ±√(-1) = ± i
So to answer ukidding's question, yes there has to be a ± 3 at 3:06 .
Because she is not asking you to solve an equation, she just gave you a number sqrt(-9).
It's actually because when it's x²+9 the ans could be 3 or -3 both it's because the quadratic rule you must have studied in class 9th that any quadratic polynomial ( where n=2) there are always 2 zeroes for that equation but here we don't need to put -3 because we have to find the value not to solve a quadratic equation
an easier way to imagine that imaginary numbers x real numbers is like even x odd even = imaginary odd = real numbers
its easy by itself so this is useless and how much time did you waste to find this comment?
edit: 0 is technically even so yeah
why does math gotta make shits like imaginary numbers t-t im suffering
It is very wrong to proceed to describe a REAL ROTATING operator as something IMAGINARY when it is all so very real.
The mathematical symbols we use are REAL OPERATORS including numbers and we must look upon them as such.
(add) (subtract) (multiply) ( divide ) ( to the power) ( roots) ( the log of ) (reciprocal) ( proportional) ( areas , volumes and lines etc) all these are REAL OPERATORS and the reader may be surprised to hear that these operators do not only work on numbers but on entities............ we can multiply a chair by a table and get a related product. It is no wonder that written somewhere in an old book, humans as man and woman were told by God to " go and multiply" . Reproduction of any creature is the product of multiplication ! but we shall not go into that. We can have two and three dimensional multiplications to produce the most wonderful meaningful and non meaningful products.
There is an operator which could be very useful to us and that is the ROTATIONAL OPERATOR which for the time being we shall call, " j ". To calibrate this operator we shall all agree that when we see the symbols " j " it will mean an anticlockwise rotation of 90 degrees , just purely a rotation to what it is associated with , while "( j^--1 or (1/j) ) is a clockwise direction. All these rotations will not interfere with the magnitude of the items that are rotated .
so (car), j(car) , jj(car) , jjj(car) , jjjj( car) would mean that a car on its wheels, one which is facing vertically to the sky, another which is upside down, one which is diving down vertically , an another which has suffered a complete rotation of 360 degrees. Note that during these operations, the car remained the same size. This sort of notations is much shorter than using spoken and written conventional sentences to describe rotations around us including a growing plant as a spiraling vine growing grapes to make wine. In the real world items do not only grow and decay in straight lines but they do spiral and rotate around as they grow and decay.
Now let us see the use of this rotation on finding the square roots. We shall define the square root as an operation, where when two exactly similar operations are conducted, then the product of this operation gives the result we want.
We can define the cube root as an operations where when three similar operations are conducted, then the products of multiplying these three operations, will give the result we want.
So if we take a pole one metre long pointing to the east described as say (pole) then doing a 90 degree rotating operating on it, now described as j(pole) this pole would be pointing North, while conducting another 90 degree operation described as jj(pole) well now the pole will be pointing to the west and we can say that
jj(pole)= -(pole) and all this means that a pole operated on by two rotations each of 90 degrees will produce a pole pointing in the other direction .
it is obvious that using normal algebra ( a pole ) on either side will cancel each other and hence jj= --1.
All these ROTATIONS are REAL, VERY REAL, and so we shall not call a rotation of 90 degrees described by "j " an imaginary number for it is a REAL operation.
Is this some form of troll comment? I mean, no offence, but your maths is flawed. In what world will having two "poles", 1 metre in length each pointing in different direction yield -1? *a* - *a* = 0, we know this. *a* - *a* =/= -1. Let *a* be the vector of the pole, where -*a* is *a* but flipped about an end of *a*. If you mean the rotated pole alone being -1m long, I still don't see the link to complex numbers.
Your description of what it means to find the square root may be confusing you. "We shall define the square root as an operation, where when two exactly similar operations are conducted, then the product of this operation gives the result we want. " - Firstly, we don't get results we want, when finding a square root, we use an input, and the outcome is what it is. Also, a square root is a number which when calculated yields a result which, if multiplied by itself, will produce the value we square rooted.
Finally, "if we take a pole one metre long pointing to the east described as say (pole) then doing a 90 degree rotating operating on it, now described as j(pole) this pole would be pointing North, while conducting another 90 degree operation described as jj(pole)" is simply wrong. the first bit is right, using your function "j", but if you perform it twice, you have 2j, not jj, or j^2, so if you did use this function twice, the result would be -(pole), but that would not be equivalent to j^2
Also, they're called imaginary numbers because of their origin. From the sound of things, you're a theist, you believe things originated owing to an action (of God). Do you question why we call sticks sticks? They don't stick to anything, it's simply a word. It means nothing other than the thing that it is, it's a title, it literally allows you to identify it, that's all. The chances are, the people who are bothered enough with maths to know about the complex plane would not think that they dimply don't exist.
Lighten up Francis.
Now just tell me what is i^(1.5)
i^(1.5)
= i^(3/2)
=(i³)^1/2
=√( i³)
=√(-i) [as i³ = i²× i= -1×i = -i]
---------- or -------
from the forth line
√(i³)
=√(i⁴/i)
=√i⁴/√i
=1/√i [as i⁴=1]
Thanks
i^18-3i^7+i^2(1+i^4)(-i)^26 solve it and give the reply
But imaginary no. R real....
sqrt (-1) = no answer
set your calculator in complex(CMPLX) mode, you will get the value
Keep doing your karma and it will come back to you one day
🙏🏾🙏🏾
no reply from father?😉😄
:)
:-)
I stopped watching your videos because you tooo fast
I want to know that what is a value of i power half
Thank you
You're welcome, Sandeep!
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Square root of -9 = error
I want to know that what is a value of i power half
thank you