@bobbrownjr
Krista, your videos are excellent. I have taught at East Georgia State College for 15 years after I retired from AT&T Bell Labs after 31 years working on satellites, fiber optics, and the first generation WI-FI. I would say about the same things to my students about imaginary numbers that you said. I would then show them that when applied to communications engineering that complex roots like a+bi and a-bi that are derived from polynomial equations give rise to sinusoidal waves that allow radios, cell phones, and fiber optic systems to be possible. We would not have television, radio, cell phones, electric cars, motors, power systems and the list goes on without imaginary numbers. As you said, these "imaginary numbers" make a lot of "real things" possible. Keep up your good work.
@godofgodseyes
Can you show me imaginary number representations with apples, oranges and bananas? Hope you can think simple things deep.
@alextl97
Your videos are very helpful, thanks.
@byteaesx1373
We could never thank you enough for your work Krista. I like the term "Lateral" better as Gauss suggested but is to late for that now.
@MatthewSuffidy
I am trying to get to the bottom of it, and I think the point is that some equations, being solved algebraically suggest a number system paradox involving a sqaure root of a negative number. You get real roots when you multiply two of these paradoxical values. I guess this suggests an imaginary number dimension that is accepted today.
@lsaackrpruto
Wow my mind just got blown. Nice narration thanks.
@heha9752
Really easy to follow! Thanks so much!
@Durfit
Do you hold your markers between your middle and ring finger? I don't recall ever seeing that before. Very helpful video though.
@indian_scouser_ynwa
excellent Krista. thank u
@leoguillon1062
Great videos, maths explained the easy way. like feynman
@Ridgerunner2270
Thanks for the refresher on imaginary numbers!
@fayadrahman552
A very sweet vivid description of imaginary numbers. Loved it! 😀
@iDigMath
i is an element of the set of complex numbers. i=(0,1) in the complex plane. The fundamental theorem of algebra shows the connection between the set of reals and it's field extension the complex numbers.
@m.d.lu.m.d9292
you are my hero <3 thanks a lot
@CE113378
Nice video! You should do a video talking about how multiplying by imaginary numbers "rotates" a number, just as multiplying by negative numbers "flips" a number (or rotates the number by 180 degrees). The concept of "rotation" may not make too much sense, until you talk about the phase difference between two quantities that are both oscillating with the same frequency. In other words, by Euler''s identity, e^(i*(omega*t + phi)) = cos(omega*t + phi) + i*sin(omega*t + phi). If a voltage and a current are both oscillating with a radial frequency omega and are phi radians out of phase with each other, and if you multiply the current by an imaginary number, then you have shifted its phase by pi/2 radians. In other words, you "rotated" it. Likewise, if your argument is a function of time (as in my example), then the number is "rotating" with time (aka - oscillating). This would kind of give an intuitive feel for what imaginary numbers actually do - in "real" life.
@sarahbracha
I'd love to hear some examples of how imaginary numbers are used in real life applications? i.e. what professions or functions are they used in, how do they actually work "in real life" since they're not actually real numbers. I mean, if there is no such number that multiplied by itself can result in a negative number, I'm having a really hard time understanding the real life use and application of imaginary numbers. Is this just math theory/philosophy? Thank you! (I'm a math teacher and will need to teach imaginary numbers later this year, so I'd really love to know what they actually are! Not just what i stands for, which I get. I want to go deeper.
@Jaimon-kw1tf
Bruh 2:35 just do square root before to subtract 4 from both sides.
@rollingrockink1
Your videos are insane, like sensory overload of arts and crafts insane. Your ability to write, produce, direct, act, edit and distribute your videos is impressive. Keep up the creative momentum. Slow down a bit though, I'm sure your subscribers would love to hear you talk more and expound upon your knowledge in the topic. Thank you for the uploads.
@courtcomposer
Well done. Thanks!
@Mattiethekorbat