OMG !!!! Eddie, I'm such a huge fan, I love your videos to learn my mathematics at home! You are a fingertip search away to learn at home and you are a great help to my success!
That last problem made me realize something neat. You can do this trick even if they’re not imaginaries. (x^2-6x+8) X^2-6x+9-9+8 (X-3)^2-1 (x-3-1)(x-3+1) (X-4)(x-2)
8:39 -- For full satisfaction at this point, I would have loved you to have the students check that the answers were correct by multiplying out the two factors (z - i)*(z - (2+5i)) to show that they do indeed give you back the original quadratic in z.
I'm not sure but i'll try. Because i = sqrt(-1), so to -4 = 4i^2, as [sqrt(anything)]^2 better give not other than anything 😉 Now we can write -3+4i = 1+4i-4, and substitute so it will be -3+4i = 1+4i+4i^2. Write 4i^2+4i+1 = 4(-1)+4i+1 (by the rule of i = sqrt(-1) and i^2 = -1). So when -3+4i = 4(-1)+4i+1, and 4(-1)+4i+1 = 4i^2+4i+1, then 4i^2+4i+1 = (2i)(2i)+(2i+2i)+(1)(1) = (2i+1)^2. Now we can see that sqrt(-3+4i) = sqrt(4i^2+4i+1) = +/-(2i+1).
Hi Eddie, so this really brings me a question whether we can square root a negative number. If we could, we are just simply assuming sqrt(-1)=i, whereas the definition of complex number is z=x+iy s.t i^2=-1
ax²+bx+c, a b and c are the coefficients This is the standard formula for a parabola/quadratic equation. Use the formula -b(-or+)ROOT(b²-4ac) Divided by. 2a Can use this formula for any 3 term that doesnt factorize neatly with prime numbers He used a calculator, you will probably get an irrational number unless the root is negative ie. ROOT(-any number)
Can Z^2 + 36 not be factored further, into z+6i and z-6i? It wasn’t done in the video, and I was wondering whether it would be wrong to do it, or whether Sir just didn’t do it
Yes, that was really the whole point of the exercise. He didn't actually write the line, but that's exactly what he's talking about when he says, "I can just write this as an (a-b), (a+b) factorization" at 10:21.
I don’t like math also not talk English but I like the way how you teach I wish when I become teacher teaching like you .
OMG !!!! Eddie, I'm such a huge fan, I love your videos to learn my mathematics at home! You are a fingertip search away to learn at home and you are a great help to my success!
That last problem made me realize something neat. You can do this trick even if they’re not imaginaries. (x^2-6x+8)
X^2-6x+9-9+8
(X-3)^2-1
(x-3-1)(x-3+1)
(X-4)(x-2)
This is called completing the square method to solve quadratic equations
That’s for solving though. And slightly different. They don’t teach this for factoring. Not at my schools they didn’t anyway.
I wish all the teachers are like you😘😘
gai ?
May be you are the world's best teacher sirr😎😊
8:39 -- For full satisfaction at this point, I would have loved you to have the students check that the answers were correct by multiplying out the two factors (z - i)*(z - (2+5i)) to show that they do indeed give you back the original quadratic in z.
2nd comment of the day!!!!!! Staying home bc am sick :(
Good Morning Sir.... I love u sir
Wao. . nice....
how is sqrt (-3 + 4*i) = +/- (1 + 2*i). I don't get it :(. And how do you take a square root of " i "?
I'm not sure but i'll try.
Because
i = sqrt(-1),
so to
-4 = 4i^2, as [sqrt(anything)]^2 better give not other than anything 😉
Now we can write
-3+4i = 1+4i-4,
and substitute so it will be
-3+4i = 1+4i+4i^2.
Write
4i^2+4i+1 = 4(-1)+4i+1 (by the rule of i = sqrt(-1) and i^2 = -1).
So when
-3+4i = 4(-1)+4i+1, and
4(-1)+4i+1 = 4i^2+4i+1, then
4i^2+4i+1 = (2i)(2i)+(2i+2i)+(1)(1) = (2i+1)^2.
Now we can see that
sqrt(-3+4i) = sqrt(4i^2+4i+1) = +/-(2i+1).
@@meikamandoliini Great! Thank You!
So for the 2nd u used completing the square method
Hi Eddie, so this really brings me a question whether we can square root a negative number. If we could, we are just simply assuming sqrt(-1)=i, whereas the definition of complex number is z=x+iy s.t i^2=-1
👍👍👍👍 First One to comment...
No
@@mustardoo98 ok
I wanna say a quote-
Alphabets in English: Dwayne Johnson.
Alphabets in Mathematics: The Rock.
what if we got z bar instead of z ??
Hello sir, how did you calculate square root of that complex number?, please help
ax²+bx+c, a b and c are the coefficients
This is the standard formula for a parabola/quadratic equation.
Use the formula -b(-or+)ROOT(b²-4ac)
Divided by. 2a
Can use this formula for any 3 term that doesnt factorize neatly with prime numbers
He used a calculator, you will probably get an irrational number unless the root is negative ie. ROOT(-any number)
@@user-vv1do1wg1j hello, I know the quadratic formula mate, i just wanted to know how he calculated square root of -3+4i at 7:28
I don't know why UA-cam is not letting me comment but I hope this helps
ua-cam.com/video/V8Q7zMBgp4E/v-deo.html
@@divyamkulshrestha5374 thank you:)
@@aagamshah8504 By the way are you in class 11th?
Good
Can Z^2 + 36 not be factored further, into z+6i and z-6i? It wasn’t done in the video, and I was wondering whether it would be wrong to do it, or whether Sir just didn’t do it
Yes
Yes, that was really the whole point of the exercise. He didn't actually write the line, but that's exactly what he's talking about when he says, "I can just write this as an (a-b), (a+b) factorization" at 10:21.
I love the Lesson how your not wearing a mask
Because he has to talk
maybe he already has took the vaccine