Complex numbers: Solving Equations (with example)
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- Опубликовано: 13 янв 2025
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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
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 :)
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
Great explanation! Easy and clear for me, even though i am not a mathematicien Keep it up professor!
Glad it helped! :)
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!
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?
Amazing explanation, I've never understood this so well ! Thank you very much !!
You are welcome!
Such a beautiful explanation... I love this channel
Du bist der Wahnsinn...! Danke für alles!
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.
dont know why but your voice makes my mind calm and relaxed. Also great video
Thank you! Explained better than my professor
Thanks it helped for my exam
Most welcome 😊
Listen Raja Sen Chowdhury is my parent.
Nice video Fabulous!
This was helpfull! Thanks
Love this video, man
Good explication, Teacher
Thank you! 😃
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
Thanks
You are welcome! I am glad that it helped :)
Thank You So Much Sir
You are very welcome :)
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.
You are amazing, Thanks
Happy to help!
Amazing video! Thank you
Thanks a lot ❤
And thank you for your support :)
Excellent thanks very much
Holy shit man thanks so much, i finally get it ❤
Nice! I am glad I could help :)
Thank you❤
You're welcome 😊
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?
I saw a similar video to this from another RUclipsr and he also made the Z^3 into polar form, but he made the terms to the right of the equality into polar form ad well….He used the form Z^n= r^n(cosvn + isinvn) and not the exponential polar form as you.
I don’t understood why he also made Z^3 into polar form. Do you have to do both sides into polar form or only the one side (2+2i)?
And also another question: what happens if you have
3z^4 + 243 = 0?
I guess you subtracts 243 on both sides and then divide 3. So you vet
Z^4= -243/4
Is this right? And do you just continue the normal path ad you showed in the video?
The exponential form is easier to deal with, in my opinion. And, yes: for 3z^4 + 243 = 0, you just subtract and divide.
I have a community forum for more questions.
@ how can I join the community forum?
And do you have to make Z^3 into polar form as well, or only the right side of the equation 2+2i?
Thanks for answering
@Footballstreamings Link in the description :)
@ thanks! How much would it cost?
@Footballstreamings You can go to Steady and see the packages. If that does not suit you, you can write me a mail.
THANKYOU SO MUCH!!!!!!!!!
tysm very helpful
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
Better than how Sal Kahn explained it, nice vid
nice ty
very good
Complex analysis??
More like foundations and calculating with numbers.
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" ?
there any one else who thinks his accent, especially for words like "rewrite", is really cute?
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: ruclips.net/video/T2D9y_77su0/видео.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. 🙂
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 :)
Solve the equation w^2=1+i............help
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Equality of complex numbers
In