A-Level Further Maths B7-01 Argand Diagram: Introducing Loci for Circles |z-a|=r

[@imasha7315]

You’re amazing sir

[@1973jdmc]

You are just FAB

[@rishadtahjeeb3678]

Thank you for the video.

[@emmaniac_the_seventeenth6088]

We all love your videos, they are incredibly useful but PLEASE PLEASE PLEASE create a playlist filing system for them so videos are easy to find. Even just an index where it is split up into some descernable order and all the topics are grouped. I'm that desperate that I'd do it for you...

[@TLMaths]

They're all organised into playlists on KZbin and organised on my website: www.tlmaths.com/home/a-level-maths/full-a-level

[@pjanedickensalves9152]

Brilliant, thank you!

[@Awai_quotes]

I have two questions is this video is the start of argand diagram and that how can i find all the videos for argand diagram in sequence.

[@TLMaths]

sites.google.com/view/tlmaths/home/a-level-further-maths/pure/b-complex-numbers/b4-introducing-the-argand-diagram

[@sid4931]

Is there loci and de moivres theorem in as level first year? or is it in second year?

[@TLMaths]

We teach loci in year 1 and de moivres theorem in year 2. Depends on how your teachers decide to run the course, but I would expect that's the most common approach.

[@Globalz_Haqq]

do we need to know this proof?

[@TLMaths]

Understand it? Yes. Regurgitate it? Probably not.

[@moodymonstrosity1423]

Is this polar coordinates

[@TLMaths]

Modulus-argument form is also sometimes called polar form. They are pretty much the same thing except Polar coordinates don't have to have anything to do with complex numbers.

[@louis4798]

@@TLMaths indeed

[@levito7783]

Quick question, at 6:26, where did the I go after you found the length of r?

[@TLMaths]

i is not included in the length of a complex number. If z = a + ib then |z| = sqrt(a^2 + b^2)

[@levito7783]

@@TLMaths ah that makes sense, thank you

[@stamfly7711]

For z = a + bi Then by definition |z| = r = sqrt(a^2 + b^2) Then |a+bi| = sqrt(a^2 + b^2) But then square both sides and a^2 + 2abi - b^2 = a^2 + b^2 But that means... abi = b^2 And... ai = b so: z = a + bi -> z = a + ai Where is my logic wrong

[@TLMaths]

"|a+bi| = sqrt(a^2 + b^2) But then square both sides and a^2 + 2abi - b^2 = a^2 + b^2" Why would squaring |a+bi| produce a^2 + 2abi - b^2? |a+bi| = sqrt(a^2 + b^2) |a+bi|^2 = a^2 + b^2

[@nosir1479]

You were treating |a+bi| algebraically. It is not to be treated as a term, rather as a notation for the length (or modulus) of the complex number, z.