visualising complex roots

[stevensiew]

absolutely what every maths student should learn

[ophello]

It would be more interesting if there was an imaginary upsidedown parabola attached at the bottom and rotated 90° so that you could track the intersection and visualize it as a consequence of an “imaginary parabola” intersecting the imaginary axis.

[ffhashimi]

I searched a lot until I found this great representation

[PHANTOMGRAPHMAN]

See my versions of this fascinating topic...
INTRO TO PHANTOM GRAPHS



y = x^2 + c showing complex roots


y=( x – 1)^2 + c showing complex roots (BEST ONE)

y = (x – 1)^2 + c showing solutions as c changes

[ahmedatifabrar]

Most books and teachers miss it out, but how instrumental it is to grasp and feel the world of complex numbers!

[marzinsouad]

Bonjour M, j'ai une question, vous avez mis le plan des nombres complexe mais à quelle distance de x=?Merci de me répondre.

[commentorchelsea]

Thank you for this wonderful presentation.

[nilsmogensen]

You are an amazing human! I have been searching for this explanation for a whole year.

[MrBmath]

Thank you so much for this video explanation. I like the imaginary numbers on their own axis, and going from the real number solutions to the complex solutions and back to the reals was very helpful. And lastly, thanks for the pause and question before increasing the c value to the point where we get complex roots; that's an excellent teaching strategy.

[eeltauy]

Oh yes! Finally! Thank you so much. A cloud was lifted from my mind.
Where can I find out more about polynomials with complex roots?

[sohinipaul]

I really appreciate u for this impressive representation . It helped me !!.. and u deserve a "thankx".

[cybervigilante]

What plotting program do you use? Sagemath has horrible complex plotting. You only get colored contour maps instead of a visual imaginary axis.

[infinityamitpandey]

How should i thx to u? I was searching for this from last 24hrs finally YouTube understand my struggle and shows ur Vedio. Thx

[marzinsouad]

Hello, you designe the plane C, how aboute the distance between x-axis and the plan C. thank you

[kabouch]

Would you please tell me what the application you are using is?

[ashish]

Which software are you using ma'am to present it???please tell🙏🙏🙏🙏

[kallekula]

Would be cooler if it wasn't just represented for the line with Real values but also with Imaginary input values to the function which would yield more of a blanket to visualize better how the function behaves with complex numbers.

[beatrizlima]

what's the name of the program she's using?

[ull]

I wonder if you could add to the animation the parabola including the imaginary roots, so that some students can see it. !!

[JulianShagworthy]

1:56 It's a second degree polynomial, so it will still have two roots, even if those roots are identical :)