Exponential form to find complex roots | Imaginary and complex numbers | Precalculus | Khan Academy

  Рет қаралды 489,422

Khan Academy

Khan Academy

Күн бұрын

Пікірлер: 112
@cpanati
@cpanati 8 жыл бұрын
Connect the 3 roots for X^3 = 1 and you get a triangle. Connect the 4 roots for X^4 = 1 and you get a square. Connect the 5 roots of X^5 = 1 and you get a pentagon. The 6 roots for X^6 = 1 and you get a hexagon. Heptagon, Octagon, et. You are now seeing the symmetry that leads into the subject of Group Theory.
@guidad542
@guidad542 5 жыл бұрын
Man, I know this is coming 2 years late but thank you! This helped me gain tremendous insight and really gain much-needed intuition!
@isaactyrone4844
@isaactyrone4844 4 жыл бұрын
Why do all the sum of all the solutions to the equation = 0?
@charleshudson5330
@charleshudson5330 4 жыл бұрын
@@isaactyrone4844 When you set an equation in X equal to zero, you are asking that equation "Where do you cross of X axis?" You are asking the equation to tell you specific information. Only the points when the equation goes across the X axis.
@isaactyrone4844
@isaactyrone4844 4 жыл бұрын
@@charleshudson5330 but let’s say I have a complex equation to the 7th power. Therefore I should get 7 solutions. Some imaginary. Some real. Why is it that the sum of all the solutions will equal 0?
@tapanbaral5862
@tapanbaral5862 3 жыл бұрын
Mind boggling
@Crossfire9211
@Crossfire9211 12 жыл бұрын
I find the repetition helps instil the information, gives myself time to get his point before he moves on. Thumbs up for every vid man, no one does this as good as you.
@zanepotts
@zanepotts 13 жыл бұрын
I learned in 10 minutes what I had been trying to learn through an entire hour and half lecture. Thanks man!!!
@c4talin94
@c4talin94 11 жыл бұрын
Man, it's 2 a.m. before a test and here you are! Saving my ass again, as you always did. I can't find the words to thank you enough!
@mojorn8837
@mojorn8837 6 жыл бұрын
c4talin94 4 years later and I’m going through the same thing!
@user-rd5nc1nb9f
@user-rd5nc1nb9f 5 жыл бұрын
@@mojorn8837 same here
@promisechuks6445
@promisechuks6445 5 жыл бұрын
5years later, at 2am on a Monday morning, I'm here doing the same thing before a test.
@Blue_Yuan
@Blue_Yuan 4 жыл бұрын
@@promisechuks6445 2months later at 1.38am morning,im here before a test dude
@kevinqu640
@kevinqu640 4 жыл бұрын
I was gonna like your comment cause I'm experiencing the same but since u got 69 likes I'm just gonna comment instead ; )
@philipbernstein5069
@philipbernstein5069 9 жыл бұрын
man, i was struggling with this in math all last week, and you made it crystal clear to me in ten minutes....great job
@shizaep
@shizaep 11 жыл бұрын
this vid is a complete bless still
@trbone76
@trbone76 12 жыл бұрын
That’s how 2pi/3 is expressed in complex numbers. cos(2pi/3) corresponds to the real part of the number because the real axis is horizontal and the cosine of an angle gives you the horizontal component. sin(2pi/3) corresponds to the imaginary part of the number because the imaginary axis is vertical and the sine of an angle gives you the vertical component. cos(2pi/3) (real) is -1/2 and sin(2pi/3) (imaginary) is sqrt(3)/2 (basic trig), so the complex number can be written as -1/2 + i*sqrt(3)/2.
@ImAllInNow
@ImAllInNow 11 жыл бұрын
Think in Tau, even more easy. 2 pi / 3 becomes tau/3 which is so obviously 1/3 of a full rotation.
@PercentageSign
@PercentageSign 9 жыл бұрын
this video is golden for EE if you never get taught this until it's too late, thank you so much
@Jemiiiimmaaa
@Jemiiiimmaaa 7 жыл бұрын
So true
@katherinemays9856
@katherinemays9856 6 жыл бұрын
This is probably the coolest thing I've ever seen.
@danieljumbo5875
@danieljumbo5875 3 жыл бұрын
He makes Maths so cool
@chickmagnent231
@chickmagnent231 12 жыл бұрын
You are GREAT!!! My math teacher is good but I cannot pay attention in class, this is the solution to my problem.
@dhinas9444
@dhinas9444 6 жыл бұрын
Well, I am not in a hurry or before a test, but i find this also nice. The explanations are so organic. Nothing stale...
@Hazit90
@Hazit90 10 жыл бұрын
this guy makes me enjoy maths. my teacher can do one.lol
@boxxer221
@boxxer221 8 жыл бұрын
Probably my favorite piece of maths. All maths should be this nice.
@yakashgoyal
@yakashgoyal 7 ай бұрын
To find the roots just use the eqn Cosx + isinx = e^ix
@ItsGazareth
@ItsGazareth 12 жыл бұрын
He calculates the cosine and sine terms from the line above.
@TheNetkrot
@TheNetkrot 4 жыл бұрын
this was nothing but great Mr Khan ... thank you so much.
@siofratowe6810
@siofratowe6810 2 жыл бұрын
what is e D:
@somebody3398
@somebody3398 12 жыл бұрын
it helps get the message through
@paulwood3460
@paulwood3460 Жыл бұрын
Complex exponentials are truly amazing 👏👏👍👍
@Phagocytosis
@Phagocytosis 12 жыл бұрын
That requires trigonometry... soh cah toa etc. Look at his trigonometry videos for explanation on that. Also, the triangles you get in this case are simple 30-60-90 triangles, so Sal just knew what the sides of that were.
@lucasm4299
@lucasm4299 9 жыл бұрын
At 2:44 where did he get "e"? Why is it here?
@ms2333
@ms2333 9 жыл бұрын
+Lucas M It comes from Euler's formula, which is e^ix=cos(x)+i*sin(x). You can imagine you can use triangles and trig functions to do this, but it ends up being simpler to let x=the angle in radians and use the e^ix form instead. This also makes it obvious why the e^i*pi=-1, which is the famous Euler's Identity.
@lucasm4299
@lucasm4299 9 жыл бұрын
+ms2333 Thanks. 4 months ago I didn't know about it. Now I have already learned about Taylor Series, and Euler's formula. Currently working on Fourier Series. I still need help with Fourier. I am also trying to understand the gradient. \/f(x,y)=
@erikdahl95
@erikdahl95 7 жыл бұрын
Also doing fourier right now, any tips on great videos or sites for learning?
@Selorm123
@Selorm123 4 жыл бұрын
Please can you do that of x^4=1?
@rismarksvej
@rismarksvej 4 жыл бұрын
I know it is Euler's magic number. However, where is the proof and evident source of it? You could say its lim(1+1/n)^n but please wait...there would be another book for that.
@lllUSlll
@lllUSlll 14 жыл бұрын
Thank You for elaborating this.
@adduun
@adduun 2 жыл бұрын
Thank you T. Sal
@P_S_42
@P_S_42 12 жыл бұрын
thank you
@miltonweinhold6859
@miltonweinhold6859 9 жыл бұрын
thank you sir
@KrunalRindani
@KrunalRindani 8 жыл бұрын
A Level Pure Maths in two days and I'm here seeing this for the first time. Anyone else in the same boat as me?
@panthar1
@panthar1 8 жыл бұрын
Not seeing it for the first time, I learned some of this in calc 2, but I must say, I did not learn this as a precalc thing.
@hqatran23
@hqatran23 12 жыл бұрын
I think I know why that happens, it's because the brain has trouble multi-tasking. He is solving the problem AND explaining at the same time, and when he tries to solve the problem in his mind, it's quite hard to talk to your audience whilst thinking!
@AstroKedde
@AstroKedde 10 жыл бұрын
thanks i get it now :) my text book is not very good at passing on its knowledge to me and i "missed "the lecture my professors gave me on the subject..
@HoshikawaHikari
@HoshikawaHikari 3 жыл бұрын
Somehow this is clearer than my paid lecture
@PandorasBox2
@PandorasBox2 7 жыл бұрын
man you are miracle worker i was so confused about this before thank you you got it all covered in less than 12 mins lol tnX again
@clinteldrickpetilla9646
@clinteldrickpetilla9646 4 жыл бұрын
Thank God
@johnnewmann2628
@johnnewmann2628 11 жыл бұрын
-pi
@ZedMusic
@ZedMusic 7 жыл бұрын
what if it was x^3+1?
@mohammadalam3021
@mohammadalam3021 6 жыл бұрын
Very helpful thanks
@jonangarcia5229
@jonangarcia5229 6 жыл бұрын
How 'bout sin(e^i)?
@ingthoringason6900
@ingthoringason6900 7 жыл бұрын
god bless you
@randeshdasanayaka257
@randeshdasanayaka257 4 жыл бұрын
hey how did u find the angle, hence the degree from 4pie/3 and from the other 2 hence what happened to the "i"
@phillies4eva
@phillies4eva 13 жыл бұрын
@xScuzzleButtx they are like place holders in an imaginary plane, for example, kinetic energy to potential energy in a spring machine. But it's most common in electrical engineering to show the relationship between potential difference (voltage) and current, in a signal.
@gatlatwal8499
@gatlatwal8499 2 жыл бұрын
Please help me calculate this Given that (√3-i) is a square root of the equation Z^9+16(1+i)z^3+a+ib=0 What is the value of a and b?
@TheCaptainshem
@TheCaptainshem 9 жыл бұрын
Hi from I am from the Philippines!
@dragonmemories
@dragonmemories 14 жыл бұрын
Im doing the DeMoivre's theorem, Is this it? I lacked behind in class and got out off place. I have a test tommorow and Im trying to do my h/w (which I have no Idea how to do) and study for a test all in one day. Is this the DeMoivre's theorem?If not where can I find it? -sorry im rushing
@Nikifuj908
@Nikifuj908 12 жыл бұрын
Yeah, 2 pi / 3 radians is just 1/3 of the way around the circle, 4 pi / 3 radians is 2/3 around, and so on.
@ashw730
@ashw730 7 жыл бұрын
when do you apply 2Pik??
@xx_faze_rolf_xxl4029
@xx_faze_rolf_xxl4029 7 жыл бұрын
complex numbers are such cancer i legit wanna smack my head onto the table untill my skull caves in
@sgurdmeal662
@sgurdmeal662 5 жыл бұрын
Complex numbers allow us to do so many things, not only that, they're extremely beutiful and interesting on their own.
@bridgeunwort61
@bridgeunwort61 3 жыл бұрын
what if the exponent isnt a whole real number? how would you come up with i , e, 3/2 solutions if it was x^i=1, x^e=1, x^3/2=1
@kyrilcouda
@kyrilcouda 4 жыл бұрын
Can I somehow use this to factor the equation into a multiplication of smaller polynomials?
@YuckFoutube85
@YuckFoutube85 11 жыл бұрын
where is the demoivre's theorem video
@orvinal2883
@orvinal2883 5 жыл бұрын
no replies in 6 years
@chanelbandit
@chanelbandit 7 жыл бұрын
Bless you
@NSAwatchesME
@NSAwatchesME 12 жыл бұрын
thanks but i dont see where the -1/2 comes from :S
@DrMudarris
@DrMudarris 4 жыл бұрын
it's the value of x coordinate in the complex plane
@jackthompson3048
@jackthompson3048 7 жыл бұрын
does e refer to Euler's number in this case?
@williamwright4813
@williamwright4813 6 жыл бұрын
Yes.
@B900
@B900 13 жыл бұрын
Amazing
@Kiyohay1
@Kiyohay1 9 жыл бұрын
Ugh, arrows in both directions on the imaginary axis hurts my eyes
@Gutesmorgen
@Gutesmorgen 12 жыл бұрын
How can Khan say its √3/2 ? Plz HELP ME!
@Jemiiiimmaaa
@Jemiiiimmaaa 7 жыл бұрын
bless u
@xScuzzleButtx
@xScuzzleButtx 13 жыл бұрын
Why are complex roots important?
@wreynolds1995
@wreynolds1995 11 жыл бұрын
Why are you telling him to shut up? You're giving him the money so that he can speak! xD
@callumgilfedder9097
@callumgilfedder9097 8 жыл бұрын
Where the hell did the x2=cos(2pi/3)+isin(2pi/3) at 8:51 come from???
@Jemiiiimmaaa
@Jemiiiimmaaa 7 жыл бұрын
Euler's formula: I can't prove it for you however whenever you see an exponential of the form e^(ix) it can be written as cos(x) + i (sin x) (There are several websites online that have the rulers formulas proof!) In this context, he's trying to find the roots of a complex number.
@ZedMusic
@ZedMusic 7 жыл бұрын
what if it was x^3+1?
@NSAwatchesME
@NSAwatchesME 12 жыл бұрын
@ 9:35 how does he get -1/2 + sqrt(3)/2 ??
@harshita1639
@harshita1639 5 жыл бұрын
It's the value of cos 120°[90+30] sin120°[90+30] I suggest u see trigo first if u still find it confusing 💜
@davidkim1340
@davidkim1340 10 жыл бұрын
so good/bad middle
@evangraham1180
@evangraham1180 10 жыл бұрын
i such likes fisics
@keenankharrat9769
@keenankharrat9769 10 жыл бұрын
I don't even care
@duhboss1
@duhboss1 13 жыл бұрын
Your videos are pretty helpful, but it's really annoying when you repeat yourself. Seriously, you say a lot of your sentences, or sentence fragments, at least two or three times before you move on.
@rgoldschmid
@rgoldschmid 12 жыл бұрын
Yeah, you should probably apologize for how annoying your voice is in the free math videos you make in your spare time for the benefit of random students you'll never see or hear from
@orvinal2883
@orvinal2883 5 жыл бұрын
shoulda used tau
@JANJAN-vw3km
@JANJAN-vw3km 5 жыл бұрын
SHUT UP
@dogeness
@dogeness 7 жыл бұрын
Can’t believe I was never taught this before... I’m taking differential equations lol...
@rithviknama
@rithviknama 6 жыл бұрын
i love you my man but that didnt help at all
@richardaversa7128
@richardaversa7128 8 жыл бұрын
Degrees... smh.
@vanessaquevedo6851
@vanessaquevedo6851 12 жыл бұрын
He may stutter but he is sure is a lot smarter than you are : )
@vbhaskar68
@vbhaskar68 8 жыл бұрын
pm
@astolfo9377
@astolfo9377 7 жыл бұрын
OH GOD 3 SECONDS IN IM BORED ALREADY
@jamesdunworth-crompton3259
@jamesdunworth-crompton3259 12 жыл бұрын
just shut up and take my money
@pragyarajput8703
@pragyarajput8703 12 жыл бұрын
lol wats dat.... u'r too slow.. umm i guess each student(indian) will feel d same,,, omg haaah
@972727277
@972727277 10 жыл бұрын
Awesome
@vbhaskar68
@vbhaskar68 8 жыл бұрын
pm
Beat Ronaldo, Win $1,000,000
22:45
MrBeast
Рет қаралды 158 МЛН
When you have a very capricious child 😂😘👍
00:16
Like Asiya
Рет қаралды 18 МЛН
Advent of Code 2024 Day 25
5:44
Jonathan Paulson
Рет қаралды 534
How to Find the nth Roots of a Complex Number with the Formula
11:27
The Math Sorcerer
Рет қаралды 101 М.
Eulers formula
8:42
Khan Academy
Рет қаралды 629 М.
Complex Numbers In Polar - De Moivre's Theorem
1:04:47
The Organic Chemistry Tutor
Рет қаралды 878 М.
Exponential Growth
16:00
Khan Academy
Рет қаралды 269 М.
Beat Ronaldo, Win $1,000,000
22:45
MrBeast
Рет қаралды 158 МЛН