Complex Numbers 1(Definition, Addition, Subtraction, Multiplication and Division of Complex Numbers)

[@user-ng9gl9xs2x]

Just watching this and I can testify that the lesson has been taught by you in a very comprehensive and understandable way for people to understand well. Thanks so much

[@jonahemmanuelofficial]

Awesome. Glad to hear

[@MelanieAmani-h2v]

Staff tech faces

[@adorer_31]

I love how your videos are always composed❤

[@jonahemmanuelofficial]

@@adorer_31 thank you so much 💙

[@FutureTechScopes]

Best tutor on CZcams❤❤❤❤
Thanks bro

[@jonahemmanuelofficial]

Always welcomed

[@divineambrose8257]

Thank you very much for the explanation Sir,very comprehensive and explanatory,my answer is
4+3i/(1-i)³=-1/4-7/4i

[@jonahemmanuelofficial]

Awesome. Welldone 👍👍👍

[@BensonVictor-tu9uv]

​@@jonahemmanuelofficialomo😢 I don't know what I'm getting wrong, I'm getting the same answer but my i is on 1/4
My answer is 7/4+1/4 i😢

[@elsa_kay]

​@@jonahemmanuelofficialI'm a new subscriber from Nigeria
my answer is -7/4+1/4i
Am I correct?

[@brandonotieno-oc7vl]

The lecture is really interesting... I've learnt a lot . thanks for detailed explanation

[@jonahemmanuelofficial]

Always welcomed
Glad to hear

[@user-pl2kq8is4q]

Sir, thank you for the explanation, very clear, all the way from Uganda. here is my answer: -2/8 +14i/8. hope i did well

[@jonahemmanuelofficial]

Awesome... Reduce it to lowest term, Welldone.

[@albiquin]

I got the same but simplified by dividing by 2...
Thanks 😊

[@TheophilusHagan-p9z]

Mr Jonah you are such a good lecturer and teacher at the same time

[@givenmusaka1500]

This is the best explanation I have ever had 🎉 thank you sir🎉

[@jonahemmanuelofficial]

Awesome.
Glad to hear.
👍👍👍👍

[@hunadipitsi8091]

You're a star sir. From South Africa 👏👏👏👏🤝🤝🙏🏻

[@NjebongBlessing]

Your the best from Cameroon thanks sir . Your students are very happy to have you sir 😊

[@jonahemmanuelofficial]

Awesome. Glad to have you here.

[@Derrobe]

Can communicate please

[@Derrobe]

Can communicate please

[@jonahemmanuelofficial]

@@Derrobe 🙏

[@akampaclinton1868]

Thanks for uo best explanation... enjoying from Kampala Uganda 🇺🇬

[@jonahemmanuelofficial]

Awesome. Happy to hear 🙏🏻

[@TheophilusHagan-p9z]

Mr Jonah you are such a good lecturer and teacher at the same time ❤

[@user-dd2dd7ds7f]

Thank you very much sir i have learned a lot of this lesson
My own answer is -2-14i/8

[@jonahemmanuelofficial]

Awesome. Glad to hear.
Reduce to the lowest term

[@Derrobe]

You are more then my lecture sir .thank you 🎉

[@jonahemmanuelofficial]

Thank you so much 👍

[@LizzyWizzy-lf5vk]

VERY CLEAR RIGHT FROM LIRA CITY, UGANDA

[@jonahemmanuelofficial]

Awesome.
Glad to have you here.

[@victoryosobor2159]

Thanks Sir 🙏
My Ans:
-2. 14
---- - ------
8. 8

[@jonahemmanuelofficial]

Awesome. Welldone 👍

[@hyginuseze5913]

Thanks so much sir for your detailed explanation

[@jonahemmanuelofficial]

Awesome.
You're welcome.

[@bonchel-p5u]

I didn't get the link pls

[@oluwaseunomogbolahantv5772]

I wished i had watched this video before i had my impromptu test on division of complex numbers
Well detailed and explanatory.. God bless you sir🙏🏾

[@jonahemmanuelofficial]

Always welcomed 👍👍

[@user-kh2wc8jf2r]

WOW u really did it well, a job well done for u hard work and effort

[@jonahemmanuelofficial]

Awesome.
Great to hear.

[@AbdulsalamMaaruf-ns3ye]

😮we really appreciate you sir 🎉🎉🎉

[@jonahemmanuelofficial]

Always welcomed. 👍

[@mufukahappy3695]

Thank you for an amazing lesson all the way from Lusaka Zambia

[@jonahemmanuelofficial]

Amazing, thank you
From Port Harcourt, Nigeria

[@learnwithsb123]

love your video so much, pls don't stop making videos . and also the link you said you will put how to calculate it with calculator

[@jonahemmanuelofficial]

It's not ready yet, when it is, I'll post

[@charityraphael7382]

Very nice video 🔥🔥🔥🔥
I got -20/16 + 10/16 i

[@jonahemmanuelofficial]

@@charityraphael7382 reduce to lowest term

[@charityraphael7382]

@@jonahemmanuelofficial alright sir thanks
I got -10/8 + 5/8 i

[@bonchel-p5u]

Thank u and my answer was-2/8 -14/8!

[@jonahemmanuelofficial]

Lowest term?

[@JJ_okonkwo]

I like your teaching boss, but we need more topics on math. I'm a university student, 100lvl

[@jonahemmanuelofficial]

👍

[@Tobechukwumishael.]

Your explanations are usually crystal clear, keep it up... ❤❤

[@jonahemmanuelofficial]

Thank you so much 🙏🙏🙏

[@ChiamaruEsther]

You are the best tutor ever

[@jonahemmanuelofficial]

Thank you so much 👍 💓

[@Alfredfreezy3]

You are a life saver, Thank you so much

[@jonahemmanuelofficial]

Awesome.
Glad to hear 🙏🏻👍👍👍

[@akinyemiidowu4557]

Wow this really fascinating, it helped a lot thank you sir.

[@jonahemmanuelofficial]

Always welcomed

[@VictoriaUdomiaye]

This was really helpful i learnt enough thanks sir💯🙏

[@wawerugichia2642]

NICE EXPLANATION FROM..... NAIROBI KENYA

[@jonahemmanuelofficial]

Awesome. Thank you. Greetings from Nigeria 👍

[@SamuelSunday-lj9bn]

Best lecturer

[@afolorunsomoyosola4362]

Thank you sir,I really enjoy your teaching 🙏🙏🙏

[@jonahemmanuelofficial]

Awesome, glad to hear 👍👍

[@ephraimkamfwa2677]

Thanks very much Sir for your help

[@jonahemmanuelofficial]

Always welcomed

[@sideeqolalekan4826]

Thanks for your astute teaching

[@jonahemmanuelofficial]

Always welcomed 🙂

[@isaiahibrahim1038]

This has helped me thank you sir

[@jonahemmanuelofficial]

Always welcomed.

[@mikeltechcenter1924]

thank you so much for the good lesson well delivered

[@jonahemmanuelofficial]

Awesome. Glad to hear

[@nwanbugudavid4419]

-2-14i/8
Thank you so much for making me understand this...

[@jonahemmanuelofficial]

Awesome. Reduce to lowest term

[@botahsprianalthomson6895]

Very educative lesson. Please, check the (1+i)^3 binomial expansion. On the i^3, why did you find -i instead of -1? Thank you

[@jonahemmanuelofficial]

Glad to hear.

[@jonahemmanuelofficial]

i³ = i × i × i
i × i = -1
-1 × i = -i

[@suhonorine7237]

You're doing a lot sir
Thank you so much

[@jonahemmanuelofficial]

Always welcomed 😊

[@godswillchuku916]

Thank you Sir

[@jonahemmanuelofficial]

Welcomed! 🙂

[@ayomideadegoke6886]

Hi sir, thank you for the comprehensive lesson. I got 1/2 +7/2 i

[@jonahemmanuelofficial]

Well-done 👍👍

[@ayomideadegoke6886]

Is it correct sir??

[@Adebende22]

Just wow
Easy to understand

[@jonahemmanuelofficial]

Awesome. Happy to hear

[@teryilaemmanuel7078]

Thank u sir for the lectures but what I got is 10/20+20/20i
reducing to the lowest
1/2+i how about it sir

[@jonahemmanuelofficial]

@@teryilaemmanuel7078 awesome. Welldone 👍

[@OribiAlabere]

The answer to the last question is -14/8 +2/8i

[@jonahemmanuelofficial]

Reduce to the lowest term

[@OribiAlabere]

@@jonahemmanuelofficial So if I reduce it to the lowest term, the answer should be -7/4 +1/4i

[@user-kl2qc9zy9f]

The best tutor🔥🔥

[@sayunijay4742]

thankyou so much ....my answer is minus 2/8 minus 14i/8

[@jonahemmanuelofficial]

Welldone

[@Itz_Jamezy_Motive]

Pls can u enlighten me on the binomial expansion formula.
The first one u applied the binomial expansion to has a +ve sign while d one u gave has a -ve sign could u pls explain how to go about it

[@jonahemmanuelofficial]

Already covered binomial expansion on this channel, do well to search it out.

[@Itz_Jamezy_Motive]

@@jonahemmanuelofficial okay.
Thanks

[@Itz_Jamezy_Motive]

@@jonahemmanuelofficial can u also explain that of arithmetic operations on complex no. In Cartesian and polar form

[@thelmaena-philips7230]

Detailed explanation tanks❤

[@jonahemmanuelofficial]

Awesome. Glad you understood

[@FawazMaruf]

Tnx sir🙏
It's well understood

[@jonahemmanuelofficial]

Awesome. Glad to hear

[@ManonoAngello]

Thanks. For the Efforts Class was kawa

[@jonahemmanuelofficial]

Great.....!!!

[@yusufsodiqdamilare5864]

-1/4 +7i/4

[@jonahemmanuelofficial]

Awesome.
Welldone. 👍👍👍

[@-KCCTV250]

Thanks I'm from Rwanda🇷🇼🇷🇼🇷🇼🇷🇼

[@jonahemmanuelofficial]

Welcomed

[@EbenezerCudjoe-mf5wt]

-2/0 -14/0i

[@jonahemmanuelofficial]

Welldone, try again, denominator can't be negative, it would be an infinite answer

[@user-bn7ig7xb9v]

This is the best

[@jonahemmanuelofficial]

Great...!!!!
Thank you so much

[@user-po7yw3po9b]

thank you so much

[@jonahemmanuelofficial]

Always welcomed

[@henrynmecha229]

Keep up the good work

[@jonahemmanuelofficial]

Surely. Thanks

[@angellakachingwe3307]

Best explaination I have ever hard 🎉thank u sir

[@jonahemmanuelofficial]

Always welcomed 👍👍

[@user-vm2ew6tv5s]

Very clear all the way from lusaka Zambia

[@jonahemmanuelofficial]

Awesome. Glad to hear

[@Givenhanchabalika]

My city

[@Derrobe]

@@Givenhanchabalika wow

[@MelanieAmani-h2v]

Weeds DT of hhfhgg

[@TriumphalDesmond]

Sir, when I tried it I got
-7/4 + (1/4)i
Pls correct me where I made mistakes 🙏

[@jonahemmanuelofficial]

Welldone .

[@TriumphalDesmond]

@@jonahemmanuelofficial thanks Sir. But am I correct?

[@AbdullahiAbdulrahuf]

@@jonahemmanuelofficial

[@MeldyNayame]

Thanks sir😊

[@jonahemmanuelofficial]

Always welcomed.

[@PraiseNegedu]

Thank you sirrr

[@jonahemmanuelofficial]

Always welcomed.

[@user-hr4uz5xd1l]

Tr thanks.

[@jonahemmanuelofficial]

Always welcomed 👍

[@brace.meee856]

Nice video sir all the way from SA ❤️

[@jonahemmanuelofficial]

Awesome.
Thank you

[@AbdulrofihAbdullahhamzah-hz3gh]

So so so interesting 🎉🎉🎉

[@jonahemmanuelofficial]

Thank you

[@JulietSunday-gs8sr]

Wow thank u sir

[@jonahemmanuelofficial]

Always welcomed 👍

[@MirabelKossy]

Thanks alot it really helped❤❤🙏🙏

[@jonahemmanuelofficial]

Awesome. Glad to hear ,👍👍👍

[@adesanwooluwafemi3433]

Thank you my answer is -2/8 -14/8i Or -1/4 -7/4i

[@jonahemmanuelofficial]

Awesome... Welldone 👍

[@charityharrison9279]

Nice explanation

[@jonahemmanuelofficial]

Great...!!!!

[@user-yt9zw3gt2q]

Sir, please the link on how to slove the algebraic complex number by using calculator

[@jonahemmanuelofficial]

Not available yet, will make

[@anywarjimmy9115]

Well presented

[@jonahemmanuelofficial]

Thank you

[@elarazzytv78]

My answer is -7/4 +2i/8
I need tour feedback sir

[@jonahemmanuelofficial]

Welldone, reduce to lowest term.

[@nyamoreangocho]

Nice sir

[@jonahemmanuelofficial]

Awesome.
Glad to hear...!!!!!

[@EmukulePatrick]

At least I can understand

[@jonahemmanuelofficial]

Great.

[@FelixPeter-mv5lf]

Thank u sir for the explanation.
But i solve it is showing me that the denominator is zero

[@jonahemmanuelofficial]

Welcomed,check your solving again

[@francisat2112]

Thanks

[@jonahemmanuelofficial]

Always welcomed 👍

[@MwansaJoy-wb9jq]

(4+3i)/(1-i)=-5/2

[@jonahemmanuelofficial]

You rationalize, not subtract

[@NelsonOguiroChrysantus-ur4es]

Thanks
My answer is 1/4 - 14i/4

[@jonahemmanuelofficial]

Welldone.
Reduce to lowest term

[@ProsperMulikhiwa]

Thus nice

[@jonahemmanuelofficial]

👍

[@MwansaJoy-wb9jq]

(4+3i)/(1-i)cubed=-2+I/2

[@jonahemmanuelofficial]

Great..!!!

[@AchoJohn-np3xo]

-4/16+6/16i

[@jonahemmanuelofficial]

Reduce to lowest term

[@TemitayoTomi-ud4in]

I love you sir ❤️❤️❤️❤️❤️

[@jonahemmanuelofficial]

Thank you, love you too 💙🙏🏻

[@user-rj6cr8en6q]

-7/4 + (1/4/)i

[@jonahemmanuelofficial]

Welldone

[@user-il8sf7un3v]

Sir please yhe link for the binomial expansion

[@jonahemmanuelofficial]

czcams.com/video/PEdVibZhj8Y/video.htmlsi=qIApW6bR-YOhZa6P

[@EsauMbamba]

Amazing, keep up the good work

[@jonahemmanuelofficial]

Surely.

[@FavourAniobi-l9c]

Sir my answer is 7-2i is it correct?

[@jonahemmanuelofficial]

Welldone 👍

[@Moscote101]

Thank you very much 😂❤

[@jonahemmanuelofficial]

Always welcomed 👍👍

[@user-rw2kq4vc1e]

Question 2
-2/8, -14/8

[@jonahemmanuelofficial]

Welldone. Reduce them to lowest term

[@Warisopeyemi-my1ld]

​@@jonahemmanuelofficial
Weldone sir
Ans: -7/4 +1/4i

[@Oconyema]

i can't see the link to the binomial expansion sir

[@jonahemmanuelofficial]

Its there.
czcams.com/video/PEdVibZhj8Y/video.htmlsi=kIUmvl4EFeSWWCb2

[@victoriaowiti1545]

Actually you made me persue my career ,can i contact you personally please sir

[@jonahemmanuelofficial]

Yes sure... Send a whatsApp message to [phone]
Go straight to the point when you DM ok?

[@MusabUmar77]

-2/8-14/8

[@jonahemmanuelofficial]

Welldone. Break it down to it's lowest term.

[@francisclifford-pb1tt]

(2) 4+3I/(1-I)^3= 22/20+4I/20

[@jonahemmanuelofficial]

Welldone.
Now reduce to lowest term

[@chiemerieemmanuel5053]

4+3i/(1-i)^3=1/2+7i/2

[@Aestheticmovieclips]

Nice video ❤️❤️❤️

[@jonahemmanuelofficial]

Awesome, thanks

[@AdebiyiAdedotun]

​@@jonahemmanuelofficialI want the link to the algebra of Complex number using calculator

[@sharonekoni3267]

Why’s the coefficient of I =-1

[@jonahemmanuelofficial]

Pleased watch the beginning of the video again

[@destinygodfrey8940]

I’m not seeing the link for the binomial expansion

[@jonahemmanuelofficial]

Please check again, I just added it

[@SamuelSunday-lj9bn]

-2/8-14i/8✓ i hope i am correct

[@abdulrasheedtijani4394]

Answer to the last example= -23-11i/26

[@jonahemmanuelofficial]

You did great, but please check your work again. More carefully this time.

[@abdulrasheedtijani4394]

I just did again answer=26+7i/29

[@PaaQwesi-oy3wg]

Ans= -7/4 +(1/4)i

[@jonahemmanuelofficial]

Welldone 👍👍👍

[@user-hm6hi9mp9r]

-2/8 - 14/8 i

[@jonahemmanuelofficial]

Reduce to its lowest term

[@user-hm6hi9mp9r]

-1/4 - 7/4 i
Thank you sir God bless you

[@jonahemmanuelofficial]

@@user-hm6hi9mp9r welldone