10 - What are Imaginary Numbers?

In this lesson, we will explore the concept of the imaginary number in algebra. We will discuss that for each new type of equation in algebra, a new type of number was needed to solve the equation. For equations involving square roots, we need the concept of the imaginary number "i", which is the square root of negative 1. In parallel with this, we know that i^2 is equal to -1. We explore how to take the square root of negative numbers using imaginary numbers and discuss their significance.

[ottofrank]

The moment this gentleman made me understand the imaginary numbers i have literally got tears in my eyes. YOU ARE A GREAT HUMAN BEING SIR! GOD BLESS YOU!

[P.Gillett]

I am a pretty old dude to be studying math, i came back to pre-algebra and saw 'i', which i vaguely remembered. after seeing all of the concepts in this video (sin, cos, etc) it is super clear to me now why they taught me 'i' in high school. Amazing explanation, for me. Though judging by the comments, I can see some guys in early high school that are being shown 'i' for the first time, without any idea about trig or calculus, this could be improved someway to make this imaginary completely understandable to grade 9 students.
Excellent work! Any high school teacher introducing students to 'i' should require this video as homework.

[machinex]

This is the first time I am seeing a math professor combining with physics professor in one man.. Awesome....

[ranka]

What a great teacher.. I feel instead of attending school, kids should just watch his video. You are great!

[edyedy]

I wish I had got a teacher/professor like you in my school/college I would have not struggled in my studies. You are a blessing. GOD bless you.

[JosephMullaney]

I get it. I get it. Thank you!

Excellent, effective, educative presentation style!

[janaa]

If only I could give this video a million likes. The explanation of imaginary numbers and how to use them was so helpful. I feel confident that I’m going to do well on my test today ;)

[Maddenzie]

been out of school for decades and have literally no use for this. BEST EXPLANATION EVER. I came here after watching a stick figure animation where he was fighting math and (i) kept coming up and I had no idea what that was. after almost giving up watching other terrible videos and guides, tried your video and I feel extremely enlightened and happy.

back in my day, these would all be "undefined". I remember that word. almost wish I was back in school to solve these and commit them to muscle memory.

ty!

[ffgenese]

Truly, you explained/presented the complex world of math in its simplest manner! Math made easy! Thank you for all of your tutorial videos!!!

[elansmith]

Wow perfect teaching, love how you show advanced math showing it’s use. Every class should do that

[felixyongco]

The Greatest.. Teacher of all times..
Love the class..

[yashwinsingh]

Thank you so much. Wasn't understanding the concept of imaginary numbers on Khan Academy, but you cleared it up thoroughly.

[adityatyagi]

You and Khan Academy are my two favorite resources for this kind of information. Thanks for everything!

[clloydmathison]

You brought significant clarity to this content for me. Thanks sir. ❤

[MARIA-and-CATS]

I loved this lecture! So clear and informative... Thank you!

[jennifercatoy]

"There's a lot more depth from what's on the board" I think is a reference to how many many boards he has

[mayyukhin]

Thank you so much, sir. I am not a maths teacher and I have difficulty in explaining about it. Your explanation greatly helps me.

[timmytim]

I appreciate all of your content. Thank you. Wish you would have been my professor for college!

[JamesSmith-uiiu]

I came here because I needed a good introductory video for my students. This is indeed a good one. However, I wish the math teacher would start with the "why" and not the "how ". My students can already solve quadratic and cubic equations when I explain imaginary numbers. I usually let them solve either of the two and, ideally, one from a real-world example.
Most importantly, I pick one that yields a solution with the square root of a negative number but has a real number solution and can be solved with some guessing. When they guessed the right solution, I then showed them how applying the concept of "i" would get them to the solution they had guessed previously. I had students who could already do all the stuff shown in this video, but they had yet to learn why they were doing it or what the problem was in the first place. Showing them the "why" first provides purpose and reason and leads them down the path of understanding there once was a problem that someone cleverly solved.

[rolandvan]

I love the great depth you go-to for all your videos