One thing I've learned in the past few months, is that I am far more capable at 'visual' learning than I am at book learning. Seeing a visual conceptualisation of certain maths problems make is so much easier to understand what is going on. The visuals are such a great compliment to the written language and really help me to grasp the abstract. I wish more of my lecturers used this method. Thankfully my calculus and statistics lecturer uses plenty of visual aids. Thanks for your work.
This applies to literally everyone. Even people who understand proofs just from reading them; they are just better at transforming it into something they grasp.
Btw, at 2:18, it does not apply to any trig function like that. It only works for this specific case. Just apply it to the e^i2pik and make it e^(i)*(2pik/n) and then treat it as feta
If you ever heard the famous identity : e^(i*Pi) + 1 = 0 which is called Euler's Identity then we can say that e^(i*Pi) = -1 so if we raise both sides to the second power then we see that e^(2*i*Pi) = 1 now if we raise both sides to the power of k then e^(2*i*Pi*k) = 1^k and since 1 raised to any power is one we can say that e^(2*i*Pi*k) = 1. Q.E.D
in diffy q atm. this was the only video that clearly explained the steps of this concept/ tysm!
Your videos look very much like Khan Academy style videos. Well done! Thank you very much!
One thing I've learned in the past few months, is that I am far more capable at 'visual' learning than I am at book learning. Seeing a visual conceptualisation of certain maths problems make is so much easier to understand what is going on. The visuals are such a great compliment to the written language and really help me to grasp the abstract. I wish more of my lecturers used this method. Thankfully my calculus and statistics lecturer uses plenty of visual aids. Thanks for your work.
Yea, but most of maths just isnt visually representable.
@@Brien831 that is the dumbest thing i have ever heard
This applies to literally everyone. Even people who understand proofs just from reading them; they are just better at transforming it into something they grasp.
Great job on this video! helped me in preparing for a complex number's test tomorrow :)
Btw, at 2:18, it does not apply to any trig function like that. It only works for this specific case. Just apply it to the e^i2pik and make it e^(i)*(2pik/n) and then treat it as feta
Really good video explaining the roots of Unity
great job. im writing a test tomorrow , this was very useful
Excellent teaching technique. I became one of your pupils.
Saved my life before finals!! Thank you!!
Thank you so much!!!
Excellent video, even though it's 10 years old!
This.....was an incredible explanation.
this video really helped me . thank you alot
Great video
You're a life saver, thanks!
Hey DA-: great videos. Flagged these when you released them and am only now reviewing. Did you retire?
great explanation !!!!!!
qebpro, i dub you Lord of the Keyboard Warriors ! *You may rise*
Ed Dy Lol
Can you tell me what software you are using for your blackboard to write your equations and draw your graphs?
..and those points can represent sampling points along a sin wave for conversion to digital.
explain Excellently .. 👌🏻
What's up with the static in the audio?
How do you find the value of k?
k varies from 0 to n. So you will have n roots. The first root is for k=0, the second for k=1, and so on up to k=n.
thanks Peter--helped me get this
@@pvadasz k will vary from 0 to n-1 to have n roots.
ok, can I show that the roots of unity for n=5 form a group under multiplication?
Great video. thanks!
Good video .Thank you !
thankk you so much. It helped me a lott...
good video!
I don't what's with me and being able to pay a lot more attention to TH-cam Teaching Videos compared to classes, both onsite or online
Brilliant
Wouldn't Z^0 also equal 1
what is the 'i' in the equation? Thanks!
i = √-1
Dunno if my comment is too late or what lol
It is the complex number
wat if r isnt 1?
Why is k always an integer?
That is how it is defined
K=1,2,3,.......n ...... it goes like this
Why is e^(i2piK) = 1 ? im lost?
If you ever heard the famous identity : e^(i*Pi) + 1 = 0 which is called Euler's Identity then we can say that e^(i*Pi) = -1 so if we raise both sides to the second power then we see that e^(2*i*Pi) = 1 now if we raise both sides to the power of k then e^(2*i*Pi*k) = 1^k and since 1 raised to any power is one we can say that e^(2*i*Pi*k) = 1. Q.E.D
why can K never exceed n??
It will trace out the points. So if n=4 and k=5, it will be the same point as k=0
Why is r = 1 again?
absolute value of 1 is 1. (1+0i)-> abs(1+0i) = sqrt (1^2+0^2) = 1 -> thus r=1
great thanks
Looks like everyone here have/had a test tomorrow/ the next day
Thanks
Sugoi
Turn your hoover off and record it again!
Couldn't watch due to the jet engine in the background