Complex Numbers, Part 1

[rualright96]

I just realized something, I LOVE YOU!! Hhahahah coming from a Freshman doing Alg ll, I thank you.

[JonathanAnonymous]

I have one question about this. Why did you put +/- before the radical?

[derekowens]

@JonathanAnonymous Because either the positive or the negative answer will work. Both are valid solutions.

[CarrieIsDaBomb]

I have a quiz in this lesson tomorrow, not to mention a Math exam next week with this lesson along with 3 other ones. I am doomed.

[TheMihai76]

what software do you use?

[DiaperedMacintosh]

which software do you use for doing the videos.

[DiaperedMacintosh]

@DiaperedMacintosh i.e writing the numbers in the form of a chalkboard or marker board.

[loopper9]

i learn better this way

[boostz32]

Thank you for explaining where any why the i is used my teacher told me "this is just what you do"

[HaikatrineKat]

Quantum Mechanics?



[HaikatrineKat]

Where do the imaginary numbers go? I mean if they're off the number line.... I'm not joking either. They exist in dark matter? I'm getting it a little better but still having trouble visualizing it... Although after watching the video I feel I've got a better understanding of this type of problem. Thanks.

[GearZNet]

Derek you should join up with Salman Khan of the KhanAcademy both of you guys are amazing teachers and could do some rather amazing things if you partnered up.

[bigknaw]

Hey. I'm an Math/Education major and I was wondering what software you are using? Thanks

[MissONTM]

so +/-i radical 2 is the same as +/- radical 2i? people just tend to regularly put "i" at the end? so it won't be wrong if I don't put "i" at the end?

[derekowens]

@MissONTM Yes, that's fine. In fact, a lot of people put the i before the radical, just so it is visually clear that the i is not under the radical. Okay either way.

[jlmdfnbo]

This video could have been compressed into 2-3 minutes, but I know how some American students can be so... still great video, saved me a lot of my free time (don't have to study this shit in class, I can sleep instead) =)

[HaikatrineKat]

@jlmdfnbo thanks man. thanks for insulting american students. get on your job hater. since you're so brilliant, why didn't you just CLEP out of algebra altogether?

[MrPinkClip]

@jlmdfnbo Why do you have to insult Americans just because your country is so incompetent?

[jlmdfnbo]

@MrPinkClip My country was voted the best country in the world by Newsweek not too long ago, I'll let you find out which one I'm talking about :)

[ThEKeeYs]

this is very easy

but thank you dod

[Deaume]

You probably hears this joke a lot, but... Derek Owns!

[mathewsgame]

if i = root negative 1 therefore i swared should be absolute value of the whole equation therefore i should = 1

[anak071]

:O ...thank you!

[ljjelly]

oh but.. i have a question that came up at about 9:20 in the video. pause it. i noticed that the 2 under the radical is plus or minus, whereas the 5 under the radical is not. is that because you are making the 2 equivalent to x the variable?

[ljjelly]

some points you get a little repetitive, but at least i learned what i needed to learn. thanks brah

[OtterChef]

Thank you SO MUCH! I'm on a total different wavelength to my further maths teacher, but this was so clear and concise, i'll be watching all your videos now :)

[Kamilk12l]

thnx u've helped me with my hmwrk ;)

[MsGenius000]

so i cubed is negative i and i to the power of 4 is 1?

[derekowens]

@MsGenius000 Yes, that's correct.

[silentsamir]

people like you are gonna revolutionize the education system ....

[jabbalicks]

got it thanks :D

[jabbalicks]

so you only put the i if the two or any number is negative?

[derekowens]

@jabbalicks Any time the number under the radical is negative. Think of it as factoring a -1 out of the number, and the square root of -1 becomes the i.

[skipstah70]

holy crap I wish I had you around in high school! I never though I was bad at math but had a very difficult time getting what was being taught back then, and as a result lost all interest. You have a great gift for explaining and keeping things interesting my friend! Share it with the world. ;)

[mharesful]

I've got an A at the "Theory of functions of a complex variable" exam. My life is now complete.

[derekowens]

@mharesful  Congratulations, and keep up the good work!

[Sylvanas17]

omg you are EPIC!!!

[Justen1980]

nice vid i am learning a lot

I am self taught in Math and am currently takin Calculus in College

the books i've read seem to favor placing i before a radical sign so it can never appear to be UNDER the radical sign

I am learning what I can on the side about Complex numbers as I'm majorin in Elec Eng and from what I understand this is an important area of math to understand

[AwesomeAy2010]

I, as an elementary mathematician, can understand this. It's AMAZING! Do you have any on Calculus?

[BACUS666]

Derek, this was the first video I saw to get me extremely interested in mathematics. My primary field of study is now mathematics, and I love complex analysis. Thank you so much, this series of videos really influenced me.

[thorne279]

You sound like george bush at the beginning.

[defenforce244]

Wow, you are a very articulate instructor. I'm actually in the military and I have one last class to "CLEP" before I finish my degree. College Math actually encompasses a lot of different things and your video helped clear up a good portion of it.. Thank you!

[alastad7]

Thanks × 1000000

[ravikanthroyss]

nice

[amazzon44]

I just watched all the segments of complex numbers and I have learned so much. Thank you so much. I will definitely be looking out for your videos. You're awesome!

[madlie3]

This is great! thanks a lot

[fonsidream]

/watch?v=MO5LgzTsI58

[samson4474]

@BoscoWins, the + or - just means that the square of any real number, + or - is positive. For example, if you have the number 9 under the radical (sq. root) sign, the answer is both 3 and -3.

[BoscoWins]

Does the plus or minus mean it can be either?

[Penndennis]

@derekowens - Derek, Thank you very much. Absolutely brilliant. Verbal and visual clarity all the way through.

Kind Regards, PD

[abs54459]

thanks it really helped me keep it up.

[GR1o6180339887498948]

This is a great start. I'll make a playlist of this series and place it on my channel too so that more people can see it.

[03Kabbotta11]

Dude, you are great. Thanks for this series.

[197001]

wtf...

Let z=x+yi. Find the values of x and y if (1-i)z=1-3i

Thats quite a simple problem... any ideas?

[airpower123]

there's not much age differnce between us.

[jaakkokuu]

Great vids. Thx alot!

[Hestrikesagain]

Dude the series of vids help me out alot!!

thank you soo much Derek!

[Excitotoxin]

Very well explained. Thank you.

[suleproductions]

im 14 can i be able to understand

[V2Force]

awsome :D now i can skip reading appendix A from my circuit book. Hm, wonder why i ever heard of complex when in cal 2 class.

[derekowens]

Calc 2 typically doesn't do any work with complex numbers. Calc 2 covers Integral calculus and infinite series, which are heady topics themselves. Complex calculus is a whole different and more difficult thing (and I don't pretend to understand it). Augustin Cauchy worked out a lot of the theory, and he was one of the great mathematicians of all time.

[Slibt]

This is off topic but, could you cover Eulers formula?

What it means, how it is derived, etc..?

[derekowens]

Oh, yeah, I'm actually planning on making a video on that soon. I'll derive the formula using differentiation, integration, and exponents, which is a smooth and elegant way to do it, although Euler actually derived it using an infinite series, which I personally find much more difficult (probably because I'm not nearly as smart at Euler).  As to what the formula means, that's harder... but I'll try!

[SmedleySmorganoff]

why does your real numberline have arrows on both ends?

[derekowens]

There are arrows on both ends because the real number line extends infinitely in both directions, with positive numbers typically to the right and negative numbers to the left. The arrows indicate that the numbers go on and on forever.

[SmedleySmorganoff]

so it's meant like that, OK thanks.

I'm just used to an Arrow on the positive side so that you can see where the pos Numbers are.

Anyways this whole video-thing is very nice work of you!

What Software/Hardware do you use to visualize your EQ's and stuff?

[derekowens]

I use a graphics tablet, a microphone, and some screen capture software, all pretty generic stuff. I've worked pretty hard at getting the process exactly right so the videos come out nice. I'm pretty happy with the results so far.

[Katsu7594]

amazing... PLEASE COME TO CPHS AND TEACH US

[boumaig]

thank u for the video

[mrpetez]

Brilliant - if every math teacher were as clear as you, this would be a much more educated world :)

[xxjacobxx3]

i agree. all teachers in general everywhere i have been dont really understand what they are talking about. its sad

[0r0chlmaru]

Thank you man! Love this tutorial. It will help me allot with my exams ;) You save my life! Keep up the good work!