I pray you're doing well during this pandemic. We're all struggling but I know we'll get through it. From all of us continuing to take classes and continuing our education during all of this, thank you.
Professor Leonard, thank you for a well explained and organized lecture/video on Creating Polynomials from Complex Solutions using the well-known complex conjugate pairs. These problems are fun and easy to solve from start to finish.
Thank you professor, anxiously waiting for the linear algebra 1 course.Currently winding up with the calculus 1 course on your channel (bliss!). You're a legend!
No, Since i^2 =-1 , in order to find i, we need to take square root on both sides. By doing so we will end up with the result i=sqrt.-1 which is not possible under real number system, so mathematicians introduced i for this
In regards to complex solutions, couldn't you just reverse engineer, a la backwards completing the square? Why create two complex factors and then distribute? Seems unnecessarily complicated? But I'm learning from ground up and do not have the benefit of seeing what's coming.
When factoring a polynomial, you can break it down to a linear function and an irreducible function for example given a function: 2x^3-x^2+2x-3 you can break it down to its factor term (2x^3-x^2+2x--3)= (x-1)*(2x^2+x+3) for x-1=0, you can see that there is an xint at 1 but for f(x)=2x^2+x+3 when you try to solve for f(x)=0, aka its x int you get a complex number, indicating that the graph of that line does not touch the x axis. hence the term irreducible quadratic because if you try to break it down even more aka factor.... you won't find solutions for it in the real term - i might be oversimplifying but I do feel I am correct here but as a note this is video no 35 out an entire lecture series so you will have to go back and watch the earlier videos to make sense of it all. best!
I'm a little bit confused on how you got x^2-2x+1+1 when you distributed at 37:36. If you could explain or link me another video that explains how you got that I would appreciate it a lot.
Thank you Professor Leonard, you are allowing us to homeschool during this pandemic. Thanks for your work and putting up videos so quickly.
This is amazing work you're doing.
I pray you're doing well during this pandemic. We're all struggling but I know we'll get through it. From all of us continuing to take classes and continuing our education during all of this, thank you.
Wonder what religion proffessor leonard believes in .
Is he an atheist or an theist ?
4:00 A Professor Leonard Promise is worth its weight in gold!
Professor Leonard, thank you for a well explained and organized lecture/video on Creating Polynomials from Complex Solutions using the well-known complex conjugate pairs. These problems are fun and easy to solve from start to finish.
Please do more differential equations videos. Thank you, prof!
Thank you professor, anxiously waiting for the linear algebra 1 course.Currently winding up with the calculus 1 course on your channel (bliss!). You're a legend!
Thank you so much for making these accessible professor, I'm kinda broke and now I'm studying math with the help of your videos
This is genius! Truly, I can't thank you enough.
You are such a good teacher. Thank you
Thanks a lot professor
thank you very much for your work!!!!! can you please continue differential equations videos? lots of people really need them
thank you
COOOL. Thank you professor.
if i^2 is -1 then wouldnt the mean -1 becomes 1 because to the power to 2.
No, Since i^2 =-1 , in order to find i, we need to take square root on both sides. By doing so we will end up with the result i=sqrt.-1 which is not possible under real number system, so mathematicians introduced i for this
thanks
In regards to complex solutions, couldn't you just reverse engineer, a la backwards completing the square? Why create two complex factors and then distribute? Seems unnecessarily complicated? But I'm learning from ground up and do not have the benefit of seeing what's coming.
I guess the more I've worked with this, the less complicated it seems.
Can someone explain what
Irreducible quadratic means
Bc I keep hearing this term, but have NO idea what it means. Thnx
When factoring a polynomial, you can break it down to a linear function and an irreducible function
for example given a function: 2x^3-x^2+2x-3
you can break it down to its factor term
(2x^3-x^2+2x--3)= (x-1)*(2x^2+x+3)
for x-1=0, you can see that there is an xint at 1
but for f(x)=2x^2+x+3 when you try to solve for f(x)=0, aka its x int you get a complex number, indicating that the graph of that line does not touch the x axis.
hence the term irreducible quadratic because if you try to break it down even more aka factor.... you won't find solutions for it in the real term
- i might be oversimplifying but I do feel I am correct here
but as a note this is video no 35 out an entire lecture series so you will have to go back and watch the earlier videos to make sense of it all.
best!
Sir, pls try to take live classes
that is what I is
Professor, do you happen to conduct research?
💖💖💖💖🔥🔥🔥🤗🤗🤗✔✔✔✔✔✔
I love you
HOW MANY OF THE SAME SHIRTS DO U HAVEEEEE lol
it's not of your business
@@whitebeardpirates7551 dude just .... *chill*
I'm a little bit confused on how you got x^2-2x+1+1 when you distributed at 37:36. If you could explain or link me another video that explains how you got that I would appreciate it a lot.
It's just distribution of the terms. What about it specifically is confusing? Maybe I can help.