Complex Numbers (Cube Roots of 1, unity) : ExamSolutions Maths Video Tutorials

Tutorial on complex numbers and the cube roots of 1.
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[@abdul-ganiyyoladele1081]

this video's really underrated

[@Ihatenicknames1]

Thank you so so much, I was looking through my textbook around 10 times not understanding this, but now I think, wow, it was that easy

[@Elkycreates]

You are better than any textbook...and I have looked at many!

[@MusanGreen]

Absolutely one of the best teachers ever. Thank you so much!

[@mmamouri]

I finally understand where 2k*Pi is coming from. Thank you!

[@ExamSolutions_Maths]

Good

[@ivornworrell]

Great Math vid, beautifully explained.

[@blissterd]

Thanks! U made it easy

[@jackwilliams4188]

Thanks, clear and easy

[@katiebell1138]

Thank you so much for making it clear that k=2 can be done, but it will take us outside the interval for Arg(Z).

[@ankitsinha4933]

awsm teaching... got exactly what i looked for... thnx sir !!!

[@Fisix_org]

Very good.. thanx. This is essential to find the roots of the cubic polynomial (ie: Cardano-DelFerro Equation)

[@stevieasdfghjklable]

you are a hero!

[@shootingstar6688]

Appreciation post- thank you very much for taking time and effort to help out us high school people! You deserve the best :) You're a great teacher and are very thorough with your explanation!

[@ExamSolutions_Maths]

Thanks for using my videos - Best wishes.

[@crash9260]

if the question is z^3 = -27/3 for example will u get an equilateral triange anyways?

[@jamesburke9865]

Thanks mate.

[@anniemoses9478]

So how will you know how many k values you should try? So for cube roots, k can be 0,1,2?

[@samoyha1]

u are soooooo better than my college math teacher...thank u soo much...appreciate it

[@sayanaufal9193]

Change profile photo

[@jackcool5798]

Your a god at teaching....... 10 out of 10

[@jackchevin187]

great video

[@ExamSolutions_Maths]

Good

[@trkingdavid4943]

thank you for ur help well explained

[@ExamSolutions_Maths]

Thank you.

[@ExamSolutions_Maths]

Pleasure.

[@ExamSolutions_Maths]

You can start with k=0 and then k=1

[@joshuaxjoseph]

you are sent from the heavens

[@tonderaitumbare6933]

thanks for good videos. what will be the angle is asked to find the 4th roots of -8

[@realFriedrichHayek]

Great video. Thanks :)

[@StressReliefPodcasts]

ur not einstein , more like epstein

[@tivakudzemagunda9638]

YadahThese videos are helpful

[@ivornworrell]

Hello, just a question plz:As I understand it, the number 1 raised to ANY power is still 1, because 1 is the multiplicative identity, so how can it be possible that the number 1 has MORE THAN one root?Thank you.

[@ikramshahzad786]

v.nice

[@johnbingham6355]

In this simplest case I suppose z*3-1 =(z-1)(z*2 +z +1) and factorize,giving the same results,

[@MegaHugoProductions]

You say that for the modulus-argument form that it is expected we use values of K that allow the argument to remain within pi and -pi. Are you expected to do this when using the exponential form? I only ask because in most formula's I see they only specify that you use values of k up to (N-1) regardless of whether the argument remains within the pi and -pi.

[@sebpaine9095]

The way we were taught it, you can just ass or take away 2 pi from the answer to get it within pi and -pi if you value of k gives an angle outside the range, as long as you show your working. (e.g if your value gives 5pi/2, just take 2pi from it to get pi/2 and state that you took 2pi from it since taking 2pi from an angle means it is geometrically identical but within the range pi and -pi)

[@edgelord9821]

Hi, if sin0 and sin2kpi is the same, why not leave it at sin0?

[@mathsgreek]

thanks for your hard work sir ! but how can i know with what values of k i will start ??

[@ivybentil8303]

Given z^n, the values of n will be 0,1,2,n-1

[@pratiksapkota5083]

maybe show the complex number powered to higher indices like 5?

[@stimulantdaimamld2099]

great

[@StressReliefPodcasts]

sukc your mom

[@sethlogosu9045]

Find the nth roots of i

[@AkhiDeia]

awesome explanation as always... thank you very much... does anyone know in what context do we use this in real life? what does the z =^1/3 means ?

[@spitalhelles3380]

If you don't know what cos(2pi/3) and sin(2pi/3) are, what do you do

[@ryanyap2807]

bonkers good

[@oyelajoshua5716]

How do we know that cos 2pi over 3 is minus half

[@StressReliefPodcasts]

omg yes!!!!! oh yeah this is what ineed in my life tahnk you so much for this video about complex number like holy cow it would be so good if u sent me 5$ on pay pal tho Pwease wink wink

[@lewisjacques]

Thanks for the video, just wondering if no matter what Z^3 is equal to, does 1+w+w^2=0 always exist as being true?
Thankyou

[@rasmusu.relling5837]

Yes, because it is a vector, the path will end up in the same point in space I guess. If you look at it as an equation.

[@MrMartin20206]

I hate how my FP teacher is a potato and cant teach AT ALL, just throwing notes at us and saying "do work". I'm gonna be so screwed for my further maths A2.

[@alfoul]

isn't the cubed root of 1 just 1? lol i'm confused

[@realFriedrichHayek]

it is but that is only on the real number line. If you look at the roots of 1 on the complex plane then there are 2 more roots

[@alfoul]

whyy

[@alfoul]

We don't take further pure math in our school so this genuinely confuses me lol

[@realFriedrichHayek]

Well the real axis is just everyday numbers used in life. e.g. 1,2,e,3,pi,4.5, sqrt2, 0, -.090221 etc.
Try rooting -1... It isnt possible using the real axis. But it is with the complex axis. We call that i. From that we can do new things with maths as we now have a 2D range of numbers. I would recommend looking at a module called FP1 to clear things up.

[@alfoul]

Hmmm, not to be annoying, but if you try to take cube root of -1 you get -1, which is why i thought the complex numbers deal with sqrt-1 only, thanks anyways bruv :D