Complex numbers: Solving Equations (with example)

[@leNnard_]

My mind is blown, you took all my confusion and replaced it with knowledge...danke für das schöne video!

[@ΘΑΝΟΣΠ-ψ1θ]

No one has ever taught me this way. Thank you, you are amazing!!

[@tortugatech]

Great explanation! Rememebered all about complex equations i forgot since freshman year

[@essayprometheus]

You are a freaking genius, i have never thought about solving complex numbers in this way. It feels like everything just makes SENSE. Thank you so much

[@estebansanchezsevilla1930]

Man its de Moivre's theorem, did u pay attention in class?

[@multimeme5935]

@@estebansanchezsevilla1930 I did pay attention, but unfortunately our teacher just write the formula and solve some problems even without any graph.

[@HDitzzDH]

It probably would've been better to explain the "1/3" part in the argument from the fact that: z = re^(iθ), thus z^3 = r^3*e^(3θ), thus 3θ = π/4 + 2π*k which means that: θ = π/12 + 2π/3*k

[@theblackswordsman8400]

This video explained waaaay better than any of my professors could have! Thank you so much! i just have a quick question regarding this explanation. At 11:25 i do not understand why you multiplied everything by 1/3 again. Could you please explain as to why you did this? thanks

[@theblackswordsman8400]

nvm i didn't see that you simply multiplied it by a 1/2 from that square root.

[@brightsideofmaths]

1/2 *1/3 = 1/6 :)

[@sohaib_mer-]

god i knew going through the exponential form was the most straightforward but NO, i set 2+2i = (a+bi)^3 and god that route was so longgggg great video keep up!

[@brightsideofmaths]

Glad it helped!

[@sgottk2928]

Awsome video, just one question In the step where you have z³ = √(8) * e^(i(π/4 + 2πk)) And then you take all to the 1/3 power to get z = √(8)^(1/3) * e^(i(π/4 + 2πk)*1/3) Over the reals, we have that for example, √x² = |x| that we can use to solve things like x²=4 |x| = √4 x = +-√4 But is there a thing that grants that √Z² = Z(k) (meaning, the results of z in function of k) over the complex plane?

[@arbenkellici3808]

Great explanation! Easy and clear for me, even though i am not a mathematicien Keep it up professor!

[@brightsideofmaths]

Glad it helped! :)

[@bridgeunwort61]

You said that the number of solutions we'll get is equal to the exponent. What if the exponent isn't a whole number, like a fraction, irrational number, or even imaginary/complex?

[@brightsideofmaths]

I only cover natural numbers as exponents here. Otherwise, everything gets much more complicated and this deserves a lot of videos then.

[@ishmealm001]

Amazing explanation, I've never understood this so well ! Thank you very much !!

[@brightsideofmaths]

You are welcome!

[@tasosrokos498]

Du bist der Wahnsinn...! Danke für alles!

[@heinminoo1618]

Thanks

[@brightsideofmaths]

You are welcome! I am glad that it helped :)

[@giorgiozannini5626]

Such a beautiful explanation... I love this channel

[@nanditadey3707]

Thanks it helped for my exam

[@brightsideofmaths]

Most welcome 😊

[@nanditadey3707]

Listen Raja Sen Chowdhury is my parent.

[@tathagatasenchowdhury3278]

Nice video Fabulous!

[@fjorland_norsk3996]

dont know why but your voice makes my mind calm and relaxed. Also great video

[@theo9362]

This was helpfull! Thanks

[@sinabeyraghdar6292]

Thank you! Explained better than my professor

[@hasnainalfarabi6420]

Thank You So Much Sir

[@brightsideofmaths]

You are very welcome :)

[@georgemaxwell6235]

tysm very helpful

[@sangachidam3219]

Excellent thanks very much

[@GeorgZiom]

Love this video, man

[@gatlatwal8499]

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?

[@offthepathworks9171]

So you wouldn't say this is precalculus? Great video as always!

[@brightsideofmaths]

I mean it's an important calculation tool but also not so simple.

[@offthepathworks9171]

@@brightsideofmaths much appreciated.

[@aminareddead]

Thanks a lot ❤

[@brightsideofmaths]

And thank you for your support :)

[@TheMounten1]

THANKYOU SO MUCH!!!!!!!!!

[@nour_780]

You are amazing, Thanks

[@brightsideofmaths]

Happy to help!

[@Ransrots]

When x is equal to 0 how would you find the argument? For example this complex equation: 0 - 7776i

[@brightsideofmaths]

Sketch the number in the complex plane and try to guess the correct angle :)

[@solomonkimba]

@@brightsideofmaths can we say 3pi/2 radian

[@pawekruczkowski7940]

Amazing video! Thank you

[@gerben880]

nice ty

[@aidanbryant154]

Better than how Sal Kahn explained it, nice vid

[@letsgo6374]

How to convert it to a+bi form? So i can plot itu

[@ΘΑΝΟΣΠ-ψ1θ]

z=re^iφ and e^iφ=cosφ + isinφ (Euler) so z = r(cosφ + isinφ) and by doing the calculations for each root (solution) , you get each of them in a+bi form

[@ShaolinMonkster]

very good

[@nanditadey3707]

I would like to support this channel

[@brightsideofmaths]

You can visit the Steady-page :) steadyhq.com/en/brightsideofmaths

[@nanditadey3707]

@@brightsideofmaths Thankyou for reminding me

[@nanditadey3707]

Can you please taught me how to do the sums of the topic: "Idea of Speed, Distance and time" ?

[@duckymomo7935]

Complex analysis??

[@brightsideofmaths]

More like foundations and calculating with numbers.

[@jimtownsend6139]

Great video, but you threw me a bit at the beginning with the pi/4 = 45 degrees.. It's kind of a sudden leap from radians to degrees.. In relation to a unit circle, Pi/4 = .7854... radians. There are 57.3 degrees in a radian, so .7854 radians X 57.3 degrees = 45 degrees.

[@brightsideofmaths]

360° - One circle: 2 Pi 180° - Half a circle: 1 Pi 90° - Quarter circle: 1/2 Pi 45° - Eighth of a circle: 1/4 Pi You do not need a calculator for that :)

[@jimtownsend6139]

Quick reply.. Thanks.. I took this over 40 years ago and with these COVID lock downs, decided to use the down time to refresh my memory :) I know the relationships, but I was thinking of someone who didn't. They would pull out a calculator type in pi/4 and get .7854... Just a small thing.. Still a great video.

[@brightsideofmaths]

@@jimtownsend6139 Yeah, of course, it is allowed to just use a calculator but I want to activate some thinking processes with my videos. I'm glad you liked the video :)

[@keytoproductivity_1915]

do u speak german? sprichst du deutsch?

[@brightsideofmaths]

Yeah, here is the German version of this video: kzbin.info/www/bejne/imOnaqyVbJymq5I

[@pervezhassan3184]

I love Germany 🥰😍also the people of Germany 😍I'm a student of mathamatics. I think also you like mathematics so if you friendly you can speak with me to discuss mathematical problem as Friend. I'm not a youtuber just visitor also learning math. So i need honest and good person to combinedly learn mathematics. As ur wish dear. Tnx. 🙂

[@imwickedd5109]

🔥🔥🔥

[@laurinwezel6577]

there any one else who thinks his accent, especially for words like "rewrite", is really cute?

[@conradasante2817]

The actal de moivrrrer say r power n but u made it power 1 over n Please check that

[@brightsideofmaths]

What do you mean? We want to calculate roots, so power 1/n :)

[@tobiaschapinda6771]

Solve the equation w^2=1+i............help

[@l3nn13]

brett

[@nunomiguel555]

Me, a pure 10 grade boi Uhh??

[@kassawbaye2752]

Equality of complex numbers

[@kassawbaye2752]

In

[@tj_1260]

ok br

[@brightsideofmaths]

yeah!