Complex numbers: Solving Equations (with example)

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This video is about solving simple equations with complex numbers, also known as extracting roots from complex numbers. There is a simple algorithm and a nice visualisation for this.
I hope that this helps students, pupils and others.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

Опубликовано:

29 сен 2024

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Комментарии : 77

@leNnard_ 4 года назад

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

@keytoproductivity_1915 4 года назад

do u speak german? sprichst du deutsch?

@brightsideofmaths 4 года назад

Yeah, here is the German version of this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-T2D9y_77su0.html

@pervezhassan3184 3 года назад

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. 🙂

@theblackswordsman8400 4 месяца назад

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 4 месяца назад

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

@brightsideofmaths 4 месяца назад

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

@bridgeunwort61 3 года назад

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 3 года назад

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

@sohaib_mer- 3 месяца назад

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 3 месяца назад

Glad it helped!

@HDitzzDH 3 года назад

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

@sgottk2928 2 года назад

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?

@ΘΑΝΟΣΠ-ψ1θ 3 года назад

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

@tortugatech 4 года назад

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

@essayprometheus 4 года назад

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 Год назад

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

@multimeme5935 3 месяца назад

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

@tathagatasenchowdhury3278 3 года назад

Nice video Fabulous!

@ishmealm001 3 года назад

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

@brightsideofmaths 3 года назад

You are welcome!

@arbenkellici3808 Год назад

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

@brightsideofmaths Год назад

Glad it helped! :)

@Ransrots 3 года назад

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

@brightsideofmaths 3 года назад

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

@solomonkimba Год назад

@@brightsideofmaths can we say 3pi/2 radian

@tasosrokos498 2 года назад

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

@heinminoo1618 4 месяца назад

Thanks

@brightsideofmaths 4 месяца назад

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

@giorgiozannini5626 4 года назад

Such a beautiful explanation... I love this channel

@theo9362 2 года назад

This was helpfull! Thanks

@gatlatwal8499 2 года назад

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?

@nanditadey3707 3 года назад

Thanks it helped for my exam

@brightsideofmaths 3 года назад

Most welcome 😊

@nanditadey3707 3 года назад

Listen Raja Sen Chowdhury is my parent.

@laurinwezel6577 Год назад

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

@offthepathworks9171 9 месяцев назад

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

@brightsideofmaths 9 месяцев назад

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

@offthepathworks9171 9 месяцев назад

@@brightsideofmaths much appreciated.

@letsgo6374 4 года назад

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

@ΘΑΝΟΣΠ-ψ1θ 3 года назад

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

@sangachidam3219 2 года назад

Excellent thanks very much

@GeorgZiom 3 года назад

Love this video, man

@fjorland_norsk3996 3 года назад

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

@tobiaschapinda6771 3 года назад

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

@nunomiguel555 3 года назад

Me, a pure 10 grade boi Uhh??

@hasnainalfarabi6420 11 месяцев назад

Thank You So Much Sir

@brightsideofmaths 11 месяцев назад

You are very welcome :)

@conradasante2817 3 года назад

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

@brightsideofmaths 3 года назад

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

@georgemaxwell6235 11 месяцев назад

tysm very helpful

@aminareddead 4 месяца назад

Thanks a lot ❤

@brightsideofmaths 4 месяца назад

And thank you for your support :)

@sinabeyraghdar6292 3 года назад

Thank you! Explained better than my professor

@duckymomo7935 4 года назад

Complex analysis??

@brightsideofmaths 4 года назад

More like foundations and calculating with numbers.

@gerben880 4 года назад

nice ty

@TheMounten1 2 года назад

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

@pawekruczkowski7940 3 года назад

Amazing video! Thank you

@tj_1260 Год назад

ok br

@brightsideofmaths Год назад

yeah!

@nour_780 Год назад

You are amazing, Thanks

@brightsideofmaths Год назад

Happy to help!

@l3nn13 2 года назад

brett

@nanditadey3707 3 года назад

I would like to support this channel

@brightsideofmaths 3 года назад

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

@nanditadey3707 3 года назад

@@brightsideofmaths Thankyou for reminding me

@nanditadey3707 3 года назад

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

@aidanbryant154 4 года назад

Better than how Sal Kahn explained it, nice vid

@ShaolinMonkster 3 года назад

very good

@jimtownsend6139 3 года назад

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 3 года назад

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 3 года назад

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 3 года назад

@@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 :)