Complex numbers: Solving Equations (with example)
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- Опубліковано 4 жов 2024
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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)
My mind is blown, you took all my confusion and replaced it with knowledge...danke für das schöne video!
No one has ever taught me this way. Thank you, you are amazing!!
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
Man its de Moivre's theorem, did u pay attention in class?
@@estebansanchezsevilla1930 I did pay attention, but unfortunately our teacher just write the formula and solve some problems even without any graph.
Great explanation! Rememebered all about complex equations i forgot since freshman year
Amazing explanation, I've never understood this so well ! Thank you very much !!
You are welcome!
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!
Glad it helped!
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
nvm i didn't see that you simply multiplied it by a 1/2 from that square root.
1/2 *1/3 = 1/6 :)
Great explanation! Easy and clear for me, even though i am not a mathematicien Keep it up professor!
Glad it helped! :)
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
Du bist der Wahnsinn...! Danke für alles!
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?
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?
I only cover natural numbers as exponents here. Otherwise, everything gets much more complicated and this deserves a lot of videos then.
Such a beautiful explanation... I love this channel
Thank you! Explained better than my professor
Thanks it helped for my exam
Most welcome 😊
Listen Raja Sen Chowdhury is my parent.
Thanks
You are welcome! I am glad that it helped :)
dont know why but your voice makes my mind calm and relaxed. Also great video
This was helpfull! Thanks
Thank You So Much Sir
You are very welcome :)
Nice video Fabulous!
Love this video, man
Thanks a lot ❤
And thank you for your support :)
Excellent thanks very much
THANKYOU SO MUCH!!!!!!!!!
Amazing video! Thank you
tysm very helpful
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?
You are amazing, Thanks
Happy to help!
nice ty
Better than how Sal Kahn explained it, nice vid
So you wouldn't say this is precalculus? Great video as always!
I mean it's an important calculation tool but also not so simple.
@@brightsideofmaths much appreciated.
When x is equal to 0 how would you find the argument? For example this complex equation: 0 - 7776i
Sketch the number in the complex plane and try to guess the correct angle :)
@@brightsideofmaths can we say 3pi/2 radian
I would like to support this channel
You can visit the Steady-page :) steadyhq.com/en/brightsideofmaths
@@brightsideofmaths Thankyou for reminding me
Can you please taught me how to do the sums of the topic: "Idea of Speed, Distance and time" ?
very good
How to convert it to a+bi form?
So i can plot itu
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
Complex analysis??
More like foundations and calculating with numbers.
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.
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 :)
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.
@@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 :)
do u speak german?
sprichst du deutsch?
Yeah, here is the German version of this video: ua-cam.com/video/T2D9y_77su0/v-deo.html
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. 🙂
there any one else who thinks his accent, especially for words like "rewrite", is really cute?
🔥🔥🔥
The actal de moivrrrer say r power n but u made it power 1 over n
Please check that
What do you mean? We want to calculate roots, so power 1/n :)
Thx you support me
Solve the equation w^2=1+i............help
brett
Equality of complex numbers
In
Me, a pure 10 grade boi
Uhh??
ok br
yeah!