Introduction to complex numbers | Imaginary and complex numbers | Precalculus | Khan Academy

Missed the previous lesson?

Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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[chinesewitholiver]

I almost gave up on quantum physics because of the mathematics, especially complex numbers. But this video gives me new hope. Finally a pixel of light at the end of the tunnel. Thanks!

[slime_entertainment_inc.]

'e is a number with which you're familiar with'. It was at this point I realised I was watching the wrong video.

[khaotik.weirdo]

I'm taking my university admission test on November and thanks to you I've learned my Math contents better than I ever could've in High School. You're really helping me build up some confidence to kick some a** in that test. You're a wonderful human being, mate. I can't wish but the best for you! Greetings from Chile.

[b._.x]

I was great at math but then they added the alphabet and i lost everything....

[jennyarachovity]

for some reason im mad, like, i have enough problems with the real numbers, why not add imaginary numbers as well! why is math like this

[__maveric__]

You guys are so awesome! Free tutoring for the sake of learning!

[sammycraigar]

It's fascinating to me that an imaginary number is essentially piggybacking on a real number, making the imaginary plane plotable at least. I've been really into Mandelbrot set recently and fractals. Thought provoking stuff.

[bigdawg_gun]

Numbers....




Then






AND NOW FREAKING ImAgInAry NuMbErS ?!?!?!

[adkadatka]

It's like Morgan Freeman narrating the lesson

[Sabagegah]

8-year-old me seeing a letter in math: 😮
18-year-old me seeing a number in math: 😱

[Daisymaow]

Nice, I have been trying to understand complex numbers and this helped out a lot!

[elrusolokooooo]

I understood many things in 4 minutes that I did not manage to understand in 16 hours of school class. And the worst thing is real life teachers get paid way more. It would be way better if teachers spent all their classes playing these videos.

[anisham]

complex numbers feel interesting after watching this video lecture!

[GhostHawk]

I’m finding this interesting! I’ve been looking around famous theorems to better my understanding of mathematics. What I am learning at school is very boring and easy. I’m 15 by the way. Can anyone recommend what direction to go in in terms of understanding more about mathematics? I would like to see what I have not learnt yet. Thank you.

[whostolemyTV]

Thank you. My University linear algebra teacher is Chinese and has a heavy accent, speeds through the lesson as well. I might as well just save my time and watch your quick videos instead of going to class

[avichalnath]

beautifully conveyed it was really helpful video LOVE FROM FIJI

[douglasposho]

thanks for the simplified explaination

[lucidfangirl]

Great, numbers have imaginary friends too! I BETTER pass this Unit Test

[ratatoolie]

i feel confident enough to pass my math test tomorrow, thanks dude <3

[vaibhavpatil]

why do we need complex nos. i mean we can do graphing with real nos too. and what is the benefit of defining a no which is sqr root of -1.pls can some1 explain ? thank u
 BTW great vdo