I found myself sitting in the college computer room saying " wow " at how easy you made this understand. I had the background knowledge from my notes and lectures, but you've put it together in such a brilliant way. For example I was confused about why K = { 1,2,3...n-1} , i.e. why it stopped at n-1... it's so clear once you spelled it out. I just took it for granted before without really digging into it. Thank you for making this a whole lot clearer.
9 minute video from some kid explains it clearer than 90 minute lecture from a well paid lecturer. It's not great when you only attend lectures to gather information on what you need to learn so you can find better material online to teach you.
Bro you are a GOD, omg i didnt understand my teacher about this topic so i searched on yt for explanation, wish you were my teacher i understood u better even if this isnt my native language!
There are 3 third roots and we get them out of the formula when k = 0, k = 1, and k =2. (Because we use k = 0, we stop at 1 less than n during the process.)
Holy shit this video helped out so much. I kept putting I in the square root and it was not going the way I wanted. Thank you so much for like a concise and easy explanation
Since there are 3 roots, there will be three seperate "lines". They will be equally spaced, so 120 degrees apart from each other. In radiants that 2pi/3.
Playlist: ua-cam.com/play/PL98E8DDDEC4FB2E55.html They go with Notes 12 on my website: www.turksmathstuff.com/math-analysis-notes.html Hope this helps!
That's one way to get there, sort of a clockwise approach. I prefer to use t + pi, where t is theta hat. if you think it through you can see that t - pi and t + pi are coterminal and differ by one rotation.
Why is it that you did not get complex conjugates for your roots? I would have expected one root at an angle of zero and the other two at 120 degrees and 240 degrees. Do I have an incorrect assumption about something?
That will happen when the number you're finding cube roots of is a positive real number because it's angle in polar will be 0 so the angle over 3 is 0, and 360/3 = 120. If the initial complex number isn't on the positive x axis it will have an angle not equal to 0 so the angle over 3 won't give 0 so the cube roots are rotated from the x-axis but still differ by 120 degrees as you rotate between them. Hope this helps!
Hello. Many thanks for getting back to me by email - and within two hours!. Would it be possible to show how you cube the answer (s) and get back to the original equation? I have tried but am doing something wrong. A video on working back from the nth roots would be great
Good explanation. Only thing I am confused on is how to check the answer as some teachers add and square the answer and take the square root to get back to "r" but you said cubing would get back to the original
In the example I did I found the cube roots so to check the answers I would want to cube what I think the cube roots are and see if I get back to the original complex number: a + bi. I think what you're talking about is finding r, which is--the way I do it--the distance from the complex number to the origin (or the absolute value of the complex number)-- and to find that I'd do sqrt(a^2 + b^2) given a + bi.
Hi! I used an app called Doceri for this video. Here's the site: www.doceri.com/ I like it and it has a few features I haven't really found in other apps.
I just rewatched and didn't see a 3pi/2 in the video. Are you talking about the 2pi/3? That comes from the fact that I'm finding cube roots, so I divide the circle (2pi) into 3 equal sectors, getting 2pi/3 and then the nth roots are separated (by rotation) by that amount. The part where you'd use pi-arctan(abs(b/a)) is what should give you 3pi/4. If you're getting that angle, you're doing it right for that part! Hope this helps! Is your user name a reference to Malazan Book of the Fallen? Just read the entire series this year. It was pretty great (if a bit long in some spots).
I'm not exactly sure what you mean, but if you're finding the nth roots, then you let k go from 0 to n-1. So cube roots has n = 3, so k = 0, 1, 2. If you go one more, to k = 3, you end up with an angle that's coterminal to when k = 0, so it's not a new, unique root.
I have no idea why my professor couldn't explain it straight forward, like this. And my books are written by my professor, so no help there. Lol. Thanks, man!
Hello, again. I went back over multiplying complex numbers and see where I was going wrong (I was separating the "real" and "imagery" numbers instead of expanding everything out of the brackets. I suppose after about the 4th power then proving the nth root by going back to the original equation will be long winded. At least I know how it works now.
I'm working from the assumption that I know the reference angle, call it z, but the actual angle is in QIII. If that's the case, then the actual angle would be pi + z. On the other hand if I wanted to go from a QIII angle to figure out it's reference angle, I would have to do angle - pi. Hope this helps!
Not sure what you mean, but I think I disagree. You could go with plus or minus, but not both. You want a unique representation of each root, not two representations of each root.
Could you potentially slow the video down? Is that something that might help you out? Like, hit the gear and pick a slower speed? If that doesn't help I'm sure there are tons of other videos out there that are slower and might help.
@@vvvxzv Well that's significantly more useful feedback, so thanks. I make these videos as a supplement for my own students and I assume kind of a lot of background knowledge because of that.
This is actually the most helpful explanation yet that I've found! Thank you!
I found myself sitting in the college computer room saying " wow " at how easy you made this understand. I had the background knowledge from my notes and lectures, but you've put it together in such a brilliant way. For example I was confused about why K = { 1,2,3...n-1} , i.e. why it stopped at n-1... it's so clear once you spelled it out. I just took it for granted before without really digging into it. Thank you for making this a whole lot clearer.
Teach my uni class, this was better than 60min spent lectures
9 minute video from some kid explains it clearer than 90 minute lecture from a well paid lecturer. It's not great when you only attend lectures to gather information on what you need to learn so you can find better material online to teach you.
My professor's lectures were giving me anxiety because it did not make any sense....this just,..... saved my life. Thank you so much!!!
Good deal. Happy to help!
Bro you are a GOD, omg i didnt understand my teacher about this topic so i searched on yt for explanation, wish you were my teacher i understood u better even if this isnt my native language!
One question, at 6:53 why do you stop at 2 when writing what k can equal?
There are 3 third roots and we get them out of the formula when k = 0, k = 1, and k =2. (Because we use k = 0, we stop at 1 less than n during the process.)
You're fast! The only complex root explanation that I found I wanted to playback at < 1x speed. Usually I want to speed it up (like with Khan Academy)
thank you! this was so helpful! i have a horrible professor, cant believe she couldn't explain something this simple
So much grateful..... ive never understood until now
How did u get theta to be 3pie over4
Where are u from
Holy shit this video helped out so much. I kept putting I in the square root and it was not going the way I wanted. Thank you so much for like a concise and easy explanation
Very good video. Clearly explained the solution. Thanks.
Really needed this , thank you so much
Sir you're a legend!
What if angle is π/6 and z complex number lie in 3rd quad
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?
This is nice and concise. Thank you for the video!
Hello , I want to ask where did we get 2pi over three in the last circle
Since there are 3 roots, there will be three seperate "lines". They will be equally spaced, so 120 degrees apart from each other. In radiants that 2pi/3.
This took a few minutes while i tried for 2 hours using my uni stuff:/ Thank u so much!
Do you have a playlist on just complex numbers ... I’ve been looking through your profile and can’t find one
Playlist: ua-cam.com/play/PL98E8DDDEC4FB2E55.html
They go with Notes 12 on my website: www.turksmathstuff.com/math-analysis-notes.html
Hope this helps!
Should θ in the third quadrant not equal "θ(hat) - π"?
That's one way to get there, sort of a clockwise approach. I prefer to use t + pi, where t is theta hat. if you think it through you can see that t - pi and t + pi are coterminal and differ by one rotation.
Thank you. That was really clear and helpful
Why is it that you did not get complex conjugates for your roots? I would have expected one root at an angle of zero and the other two at 120 degrees and 240 degrees. Do I have an incorrect assumption about something?
That will happen when the number you're finding cube roots of is a positive real number because it's angle in polar will be 0 so the angle over 3 is 0, and 360/3 = 120. If the initial complex number isn't on the positive x axis it will have an angle not equal to 0 so the angle over 3 won't give 0 so the cube roots are rotated from the x-axis but still differ by 120 degrees as you rotate between them. Hope this helps!
@@turksvids Thank you for clarifying!
Hello. Many thanks for getting back to me by email - and within two hours!. Would it be possible to show how you cube the answer (s) and get back to the original equation? I have tried but am doing something wrong. A video on working back from the nth roots would be great
Good explanation. Only thing I am confused on is how to check the answer as some teachers add and square the answer and take the square root to get back to "r" but you said cubing would get back to the original
In the example I did I found the cube roots so to check the answers I would want to cube what I think the cube roots are and see if I get back to the original complex number: a + bi. I think what you're talking about is finding r, which is--the way I do it--the distance from the complex number to the origin (or the absolute value of the complex number)-- and to find that I'd do sqrt(a^2 + b^2) given a + bi.
Great video and explanation. Thank you!
Is 3rd root the same with 3rd principal of a complex number???
Can you give an example of what you mean? (I don't think I understand the question.)
Simple n good explanation!! Thanks.
That did make tone of sense. Thanks
That was supposed to be "ton" , my bad.
Thank You. This helped a lot!
good explaination ......
Can I ask...what software do you use to make your notes? I would really like to use it for my videos. Thank you :)
Hi! I used an app called Doceri for this video. Here's the site: www.doceri.com/
I like it and it has a few features I haven't really found in other apps.
Great explanation!!!
how is the angle 3pi/2? if you do pi - tan^-1(b/a) I get something different
I just rewatched and didn't see a 3pi/2 in the video. Are you talking about the 2pi/3? That comes from the fact that I'm finding cube roots, so I divide the circle (2pi) into 3 equal sectors, getting 2pi/3 and then the nth roots are separated (by rotation) by that amount.
The part where you'd use pi-arctan(abs(b/a)) is what should give you 3pi/4. If you're getting that angle, you're doing it right for that part!
Hope this helps! Is your user name a reference to Malazan Book of the Fallen? Just read the entire series this year. It was pretty great (if a bit long in some spots).
@@turksvids I actually meant 3pi/4, I was doing the calculation wrong and using tan instead of inverse tan. And yeah, name is because of the books
Thank you very clear explanation 🙂👍
How the values of k are 0 1 2 at last??
I'm not exactly sure what you mean, but if you're finding the nth roots, then you let k go from 0 to n-1. So cube roots has n = 3, so k = 0, 1, 2. If you go one more, to k = 3, you end up with an angle that's coterminal to when k = 0, so it's not a new, unique root.
THANK YOUUU SO MUCHHH🥺🥺
This is vid is just extremely helpful
Which software u are using
Doceri on an iPad with a stylus. There's also a windows app, I'm pretty sure.
@@turksvids how can I install it?
Same as any other app, really. Here's the link: doceri.com/
Very interesting video.
can you prove all this law that you are using here ?
It's an extension of DeMoivre's Theorem: en.wikipedia.org/wiki/De_Moivre%27s_formula
Great explanation. Thank you so much.
Good stuff
I have no idea why my professor couldn't explain it straight forward, like this. And my books are written by my professor, so no help there. Lol.
Thanks, man!
You explained it very nicly.
Thanks
Hello, again. I went back over multiplying complex numbers and see where I was going wrong (I was separating the "real" and "imagery" numbers instead of expanding everything out of the brackets. I suppose after about the 4th power then proving the nth root by going back to the original equation will be long winded. At least I know how it works now.
Thank you
awesome video. thanks a lot
Thanks man....
what software do u use to make these videos ?
Doceri on an iPad. I also use a cheap stylus from amazon.
(doceri.com/)
at 1:42 I swear that quadrants argument is theta-pi
I'm working from the assumption that I know the reference angle, call it z, but the actual angle is in QIII. If that's the case, then the actual angle would be pi + z. On the other hand if I wanted to go from a QIII angle to figure out it's reference angle, I would have to do angle - pi.
Hope this helps!
Meanwhile, the khan academy video is a whole hour lol. In 8 minutes you learn more then you do from sal in his long ass video
really helpful, thanks a lot
Thank you so much
How did people down vote this
congratz man
Turk the UA-camr
Post in 2016 and I just clear in 2019
gotta love how math is timeless ;)
helpful.........................
here the value of k will be plus minus
Not sure what you mean, but I think I disagree. You could go with plus or minus, but not both. You want a unique representation of each root, not two representations of each root.
bless
thank you!!!!
❤️
Ok now how is it going to help me in real life situations? 🙂
add 0i to your situation and make it complex
You're just rushing through everything ffs
Could you potentially slow the video down? Is that something that might help you out? Like, hit the gear and pick a slower speed? If that doesn't help I'm sure there are tons of other videos out there that are slower and might help.
@@turksvids it's more that you're saying a value without saying how you got that sometimes. Just abit confusing
@@vvvxzv Well that's significantly more useful feedback, so thanks. I make these videos as a supplement for my own students and I assume kind of a lot of background knowledge because of that.
Not good for a beginner
It's not exactly a beginner topic though, to be fair...Assume's a bunch of prior knowledge of complex numbers and algebraic concepts.