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

[emmaniac_the_seventeenth]

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...

[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.

[sid]

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

[stamfly]

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

[levito]

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