How to write complex numbers in polar form
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- Опубліковано 18 кві 2019
- This video shows you how to change complex numbers from cartesian form to polar form. You will learn how to convert complex numbers in cartesian form to polar form.
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I’ve watched like 4 videos on this and this is the one that finally made it “click” thanks so much!
I'm glad the video helped. Complex numbers are a bit tricky but they're very useful in maths at higher level. Thank you for your comment, I appreciate the feedback and wish you all the best with your studies.
Very clear explanation with just the right pace. Thank you.
I’m glad the video was helpful. Best of luck with your studies.
Amazing video really good explanation you explain everything you’re doing really well and leave nothing unknown
Thank you. I'm glad you found the video helpful. Best of luck with your studies.
Wow i was in so much stress because i could not understand this polar form thing but you just made it so simple and easy to understand,thank for the work that your doing,God bless your brother.
I'm glad the video helped and wish you all the best with your studies 👍
Thank you very much. Clear and concise explaination. Cheers!
No problem. Glad the video helped👍
Thanks for the video, super helpful stuff.
I'm very pleased the video was helpful. All the best with your studies.
Very helpful, thanks!
Glad it was helpful. Best of luck with your maths 👍
Do we use general argument when finding polar equivalent or is it a must or a standard to use principal arguments?
It is standard to use the principle argument which is the fraction in it's lowest form. For example, cos(pi/4) is the same as cos(9pi/4) and cos( 17pi/4) etc, the only difference is that 2*pi has been added to take account of one revolution around the unit circle. However your teacher might be asking you to consider the odd and even nature of sine and cosine functions. For example cos(pi/4) is the same as cos(minus pi/4), which is also the same as cos (7pi/4). I would need to make a separate video to cover this but you can find out more information if you research the properties of the unit circle.
@@DavidWrightUK ohh.
I now understand.
Thanks a lot.
For any complex number is it always r(cos theta + sin theta)??
Yes, but note that it is i * sin theta. So if a complex number (which we call z) is of the form z = a + bi (where a and b are real numbers), then in polar form we have z = r(cos theta + i * sin theta), where r is the modulus of z and theta is an argument of z. Hope this helps.
Thankuu so much for clear my douts🙏🏼☺️
I'm really pleased the video helped. Thanks for leaving a comment.
Explained it way better than my teacher did
That's good to hear. Many thanks 👍
Thanks, graet video. Is there a way to go about it without having to plot a graph
The graph is just a tool to help you picture the problem. With practice you can do this in your mind without drawing the graph. Lots of maths is like this and some mathematicians prefer visual methods whilst others are more algebra based.
The Cos -π/4 didn't give me 2 so how'd you get yours??
You have to make sure your calculator is set in radians. You also might be getting an answer that is equivalent. For example 1/sqrt(2) is the same as sqrt(2)/2.
love this 🤩
Thank you 👍
If we write complex form of (-1) then theta should be 0 since tan theta will also be 0, but when I convert it in my calculator it says theta is 180.Why is this happening?
My video entitled "what are radians" might help, see ua-cam.com/video/8JaVHwgNU-g/v-deo.html . If you read about the "unit circle" then it will help you to see why -1 has an angle of 180 or pi radians.
Thank you!!!💙💙💙
You're welcome 😎
Pls assist when I am pressing on my calculator it is not giving me, can u just show us how do u press on ur calculator
You need to make sure your calculator is set to radians. Press "shift", "set up", then "Rad".
Thanks ❤❤❤
On point 📌
Appreciated, thank you 👍
6/1/2024
Thank you
You're welcome :)
Well explained
Thank you
If you wrote it was 7 pi/4 would that work?
7 pi/4 is mathematically equivalent but it depends on whether your course requires angles to be determined between 0 to 2pi or between 0 to pi and 0 to minus pi. In the UK, most courses work on 0 to pi or 0 to minus pi but this might be different depending on where you live. It’s therefore best to check with your teacher. Hope this helps.
@@DavidWrightUK Thanks for the response. I think either one would be fine depending on the teachers requirements. I was just wondering whether a coternimal angle for a complex number would still be mathematically correct.
Thank you
Thanks!
You're welcome :)
Thankssssss 🤗
No problem 👍
thanks
You're welcome!
Thank u w❤❤❤❤❤❤❤
No problem 👍
Could you work on the voice sound
This is a good point, and is especially true on my videos that are a few years old and were recorded on a phone. My newer videos are made using video editing software and the sound quality is much better. I totally get your point about the older stuff.
Aren't you to add 2π to -π/4?
I've solved it differently and this is my result:
Z = 2sqrt(2) (cos(7π/4) + isin(7π/4))
The two answers are equivalent because the difference is 2*pi as you've mentioned. Some university courses want an answer between 0 and 2 pi, whilst others want answers from 0 to pi / 0 to minus pi. There isn't a standard convention for this which is why sometimes you will get different (but equivalent) answers in this type of problem.
Why have we gone in a negative direction? That’s what I’m failing to understand. If we are working in the 3rd and 4th quadrant are we going in a negative direction?
And how would you do one in the third quadrant?
It is convention to regard the third and fourth quadrant as the negative direction so that none of the angles are more than plus or minus pi.
@@DavidWrightUK thank you. Lost sleep over this question haha
I love u
Voice is blurred
Thank you.
Clear video but when I punch on my calculator I don't get the same answers
Is your calculator set to work in radians? It’s probably set to degrees if you’re getting different answers.
you talk so slow lmao I have the video in 1.75x speed and it’s perfectly normal now
It's good that UA-cam allows the speed to be changed. Some people like the slow speed, others don't - so it's just one of those things that doesn't quite match everyone's need. Changing the speed is a good solution - especially for viewers who speak English as their native language.